diff --git "a/cube1/test.jsonl" "b/cube1/test.jsonl" new file mode 100644--- /dev/null +++ "b/cube1/test.jsonl" @@ -0,0 +1,502 @@ +{"sample_id": "C001", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "S"], "observed_path_faces": [{"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C001_path_sequence.png"}, "metadata": {"level_id": 1, "name": "Reconstruct 001", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-001.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["4", "G", "smile", "5", "4", "triangle"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "4", "rotation": 90}, "BOTTOM": {"patternId": "triangle", "rotation": 90}, "FRONT": {"patternId": "G", "rotation": 90}, "BACK": {"patternId": "5", "rotation": 0}, "LEFT": {"patternId": "4", "rotation": 270}, "RIGHT": {"patternId": "smile", "rotation": 180}}, "bottom_faces": [{"patternId": "triangle", "rotation": 90, "x": 1, "y": 2}, {"patternId": "5", "rotation": 180, "x": 1, "y": 1}, {"patternId": "smile", "rotation": 0, "x": 2, "y": 1}, {"patternId": "triangle", "rotation": 180, "x": 2, "y": 2}], "slot_sequence": ["BACK", "RIGHT", "BOTTOM"], "required_slots": ["BACK", "RIGHT", "BOTTOM"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "triangle", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "5", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "smile", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "triangle", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "5", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "smile", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C001\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=5, rotation=180, flipVertical=true\n- step 2: patternId=smile, rotation=0, flipVertical=true\n- step 3: patternId=triangle, rotation=180, flipVertical=true\n- allowed patternId values for this task: 5, smile, triangle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C001"} +{"sample_id": "C002", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E"], "observed_path_faces": [{"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C002_path_sequence.png"}, "metadata": {"level_id": 2, "name": "Reconstruct 002", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-002.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["2", "diamond", "M", "6", "3", "U"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "2", "rotation": 90}, "BOTTOM": {"patternId": "U", "rotation": 270}, "FRONT": {"patternId": "diamond", "rotation": 180}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 270}, "RIGHT": {"patternId": "M", "rotation": 270}}, "bottom_faces": [{"patternId": "U", "rotation": 270, "x": 1, "y": 1}, {"patternId": "diamond", "rotation": 180, "x": 1, "y": 2}, {"patternId": "M", "rotation": 270, "x": 2, "y": 2}], "slot_sequence": ["FRONT", "RIGHT"], "required_slots": ["FRONT", "RIGHT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C002\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=diamond, rotation=180, flipVertical=true\n- step 2: patternId=M, rotation=270, flipVertical=true\n- allowed patternId values for this task: diamond, M, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C002"} +{"sample_id": "C003", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "W"], "observed_path_faces": [{"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C003_path_sequence.png"}, "metadata": {"level_id": 3, "name": "Reconstruct 003", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-003.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["2", "heart", "arrow_left", "1", "H", "star"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "2", "rotation": 180}, "BOTTOM": {"patternId": "star", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 0}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "H", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 0}}, "bottom_faces": [{"patternId": "star", "rotation": 0, "x": 1, "y": 1}, {"patternId": "heart", "rotation": 0, "x": 1, "y": 2}, {"patternId": "arrow_left", "rotation": 0, "x": 2, "y": 2}, {"patternId": "heart", "rotation": 0, "x": 1, "y": 2}], "slot_sequence": ["FRONT", "RIGHT", "FRONT"], "required_slots": ["FRONT", "RIGHT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C003\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=heart, rotation=0, flipVertical=true\n- step 2: patternId=arrow_left, rotation=0, flipVertical=true\n- step 3: patternId=heart, rotation=0, flipVertical=true\n- allowed patternId values for this task: heart, arrow_left, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C003"} +{"sample_id": "C004", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "W"], "observed_path_faces": [{"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C004_path_sequence.png"}, "metadata": {"level_id": 4, "name": "Reconstruct 004", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-004.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["C", "square", "N", "E", "E", "H"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "C", "rotation": 180}, "BOTTOM": {"patternId": "H", "rotation": 90}, "FRONT": {"patternId": "square", "rotation": 0}, "BACK": {"patternId": "E", "rotation": 270}, "LEFT": {"patternId": "E", "rotation": 180}, "RIGHT": {"patternId": "N", "rotation": 270}}, "bottom_faces": [{"patternId": "H", "rotation": 90, "x": 3, "y": 1}, {"patternId": "square", "rotation": 0, "x": 3, "y": 2}, {"patternId": "E", "rotation": 180, "x": 2, "y": 2}, {"patternId": "E", "rotation": 270, "x": 1, "y": 2}], "slot_sequence": ["FRONT", "LEFT", "BACK"], "required_slots": ["FRONT", "LEFT", "BACK"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 0}, "BACK": {"patternId": "E", "rotation": 90}, "LEFT": {"patternId": "E", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 0}, "BACK": {"patternId": "E", "rotation": 90}, "LEFT": {"patternId": "E", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C004\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=square, rotation=0, flipVertical=true\n- step 2: patternId=E, rotation=180, flipVertical=true\n- step 3: patternId=E, rotation=270, flipVertical=true\n- allowed patternId values for this task: square, E, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C004"} +{"sample_id": "C005", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N"], "observed_path_faces": [{"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C005_path_sequence.png"}, "metadata": {"level_id": 5, "name": "Reconstruct 005", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-005.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_right", "9", "arrow_right", "M", "arrow_left", "N"], "start_x": 2, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "arrow_right", "rotation": 180}, "BOTTOM": {"patternId": "N", "rotation": 270}, "FRONT": {"patternId": "9", "rotation": 270}, "BACK": {"patternId": "M", "rotation": 180}, "LEFT": {"patternId": "arrow_left", "rotation": 180}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}}, "bottom_faces": [{"patternId": "N", "rotation": 270, "x": 2, "y": 2}, {"patternId": "arrow_left", "rotation": 90, "x": 1, "y": 2}, {"patternId": "M", "rotation": 90, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "BACK"], "required_slots": ["LEFT", "BACK"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C005\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_left, rotation=90, flipVertical=true\n- step 2: patternId=M, rotation=90, flipVertical=true\n- allowed patternId values for this task: arrow_left, M, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C005"} +{"sample_id": "C006", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E"], "observed_path_faces": [{"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C006_path_sequence.png"}, "metadata": {"level_id": 6, "name": "Reconstruct 006", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-006.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["star", "Z", "R", "arrow_right", "U", "A"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 3, "true_solution_faces": {"TOP": {"patternId": "star", "rotation": 180}, "BOTTOM": {"patternId": "A", "rotation": 90}, "FRONT": {"patternId": "Z", "rotation": 0}, "BACK": {"patternId": "arrow_right", "rotation": 270}, "LEFT": {"patternId": "U", "rotation": 90}, "RIGHT": {"patternId": "R", "rotation": 0}}, "bottom_faces": [{"patternId": "A", "rotation": 90, "x": 1, "y": 1}, {"patternId": "R", "rotation": 90, "x": 2, "y": 1}, {"patternId": "star", "rotation": 0, "x": 3, "y": 1}], "slot_sequence": ["RIGHT", "TOP"], "required_slots": ["RIGHT", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "star", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C006\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=R, rotation=90, flipVertical=true\n- step 2: patternId=star, rotation=0, flipVertical=true\n- allowed patternId values for this task: R, star, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C006"} +{"sample_id": "C007", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "E"], "observed_path_faces": [{"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C007_path_sequence.png"}, "metadata": {"level_id": 7, "name": "Reconstruct 007", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-007.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["I", "4", "7", "Z", "triangle", "T"], "start_x": 1, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "I", "rotation": 0}, "BOTTOM": {"patternId": "T", "rotation": 180}, "FRONT": {"patternId": "4", "rotation": 90}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "triangle", "rotation": 270}, "RIGHT": {"patternId": "7", "rotation": 270}}, "bottom_faces": [{"patternId": "T", "rotation": 180, "x": 1, "y": 3}, {"patternId": "Z", "rotation": 90, "x": 1, "y": 2}, {"patternId": "I", "rotation": 0, "x": 1, "y": 1}, {"patternId": "7", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["BACK", "TOP", "RIGHT"], "required_slots": ["BACK", "TOP", "RIGHT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "I", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "7", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "7", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C007\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Z, rotation=90, flipVertical=true\n- step 2: patternId=I, rotation=0, flipVertical=true\n- step 3: patternId=7, rotation=180, flipVertical=true\n- allowed patternId values for this task: Z, I, 7, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C007"} +{"sample_id": "C008", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "W"], "observed_path_faces": [{"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C008_path_sequence.png"}, "metadata": {"level_id": 8, "name": "Reconstruct 008", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-008.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["O", "D", "arrow_up", "I", "N", "diamond"], "start_x": 2, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "diamond", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 270}, "BACK": {"patternId": "I", "rotation": 0}, "LEFT": {"patternId": "N", "rotation": 270}, "RIGHT": {"patternId": "arrow_up", "rotation": 90}}, "bottom_faces": [{"patternId": "diamond", "rotation": 0, "x": 2, "y": 3}, {"patternId": "I", "rotation": 180, "x": 2, "y": 2}, {"patternId": "O", "rotation": 270, "x": 2, "y": 1}, {"patternId": "N", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["BACK", "TOP", "LEFT"], "required_slots": ["BACK", "TOP", "LEFT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 180}, "LEFT": {"patternId": "N", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 180}, "LEFT": {"patternId": "N", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C008\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=I, rotation=180, flipVertical=true\n- step 2: patternId=O, rotation=270, flipVertical=true\n- step 3: patternId=N, rotation=0, flipVertical=true\n- allowed patternId values for this task: I, O, N, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C008"} +{"sample_id": "C009", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "W", "N"], "observed_path_faces": [{"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C009_path_sequence.png"}, "metadata": {"level_id": 9, "name": "Reconstruct 009", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-009.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["B", "F", "A", "Z", "8", "heart"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "B", "rotation": 270}, "BOTTOM": {"patternId": "heart", "rotation": 180}, "FRONT": {"patternId": "F", "rotation": 270}, "BACK": {"patternId": "Z", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 180}, "RIGHT": {"patternId": "A", "rotation": 0}}, "bottom_faces": [{"patternId": "heart", "rotation": 180, "x": 1, "y": 2}, {"patternId": "A", "rotation": 90, "x": 2, "y": 2}, {"patternId": "heart", "rotation": 180, "x": 1, "y": 2}, {"patternId": "Z", "rotation": 180, "x": 1, "y": 1}], "slot_sequence": ["RIGHT", "BOTTOM", "BACK"], "required_slots": ["RIGHT", "BOTTOM", "BACK"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "heart", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "Z", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "A", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "heart", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "Z", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "A", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C009\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): E -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=A, rotation=90, flipVertical=true\n- step 2: patternId=heart, rotation=180, flipVertical=true\n- step 3: patternId=Z, rotation=180, flipVertical=true\n- allowed patternId values for this task: A, heart, Z, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C009"} +{"sample_id": "C010", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W"], "observed_path_faces": [{"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C010_path_sequence.png"}, "metadata": {"level_id": 10, "name": "Reconstruct 010", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-010.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["smile", "arrow_up", "U", "T", "2", "square"], "start_x": 2, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "smile", "rotation": 180}, "BOTTOM": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "arrow_up", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 270}, "LEFT": {"patternId": "2", "rotation": 90}, "RIGHT": {"patternId": "U", "rotation": 180}}, "bottom_faces": [{"patternId": "square", "rotation": 90, "x": 2, "y": 2}, {"patternId": "T", "rotation": 90, "x": 2, "y": 1}, {"patternId": "2", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["BACK", "LEFT"], "required_slots": ["BACK", "LEFT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 90}, "LEFT": {"patternId": "2", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 90}, "LEFT": {"patternId": "2", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C010\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=T, rotation=90, flipVertical=true\n- step 2: patternId=2, rotation=270, flipVertical=true\n- allowed patternId values for this task: T, 2, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C010"} +{"sample_id": "C011", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W"], "observed_path_faces": [{"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C011_path_sequence.png"}, "metadata": {"level_id": 11, "name": "Reconstruct 011", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-011.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["star", "H", "1", "triangle", "plus", "W"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "star", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 90}, "FRONT": {"patternId": "H", "rotation": 180}, "BACK": {"patternId": "triangle", "rotation": 270}, "LEFT": {"patternId": "plus", "rotation": 90}, "RIGHT": {"patternId": "1", "rotation": 90}}, "bottom_faces": [{"patternId": "W", "rotation": 90, "x": 2, "y": 1}, {"patternId": "H", "rotation": 180, "x": 2, "y": 2}, {"patternId": "plus", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["FRONT", "LEFT"], "required_slots": ["FRONT", "LEFT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "plus", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "plus", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C011\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=H, rotation=180, flipVertical=true\n- step 2: patternId=plus, rotation=90, flipVertical=true\n- allowed patternId values for this task: H, plus, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C011"} +{"sample_id": "C012", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "N"], "observed_path_faces": [{"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C012_path_sequence.png"}, "metadata": {"level_id": 12, "name": "Reconstruct 012", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-012.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["triangle", "2", "L", "5", "Z", "plus"], "start_x": 1, "start_y": 1, "grid_width": 3, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "triangle", "rotation": 180}, "BOTTOM": {"patternId": "plus", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "5", "rotation": 90}, "LEFT": {"patternId": "Z", "rotation": 90}, "RIGHT": {"patternId": "L", "rotation": 90}}, "bottom_faces": [{"patternId": "plus", "rotation": 0, "x": 1, "y": 1}, {"patternId": "2", "rotation": 270, "x": 1, "y": 2}, {"patternId": "plus", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["FRONT", "BOTTOM"], "required_slots": ["FRONT", "BOTTOM"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "plus", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "plus", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C012\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=2, rotation=270, flipVertical=true\n- step 2: patternId=plus, rotation=0, flipVertical=true\n- allowed patternId values for this task: 2, plus, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C012"} +{"sample_id": "C013", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "W"], "observed_path_faces": [{"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C013_path_sequence.png"}, "metadata": {"level_id": 13, "name": "Reconstruct 013", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-013.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["W", "W", "T", "P", "R", "K"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "W", "rotation": 270}, "BOTTOM": {"patternId": "K", "rotation": 90}, "FRONT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "P", "rotation": 270}, "LEFT": {"patternId": "R", "rotation": 270}, "RIGHT": {"patternId": "T", "rotation": 0}}, "bottom_faces": [{"patternId": "K", "rotation": 90, "x": 3, "y": 1}, {"patternId": "R", "rotation": 180, "x": 2, "y": 1}, {"patternId": "W", "rotation": 0, "x": 2, "y": 2}, {"patternId": "W", "rotation": 180, "x": 1, "y": 2}], "slot_sequence": ["LEFT", "FRONT", "TOP"], "required_slots": ["LEFT", "FRONT", "TOP"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "W", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "W", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C013\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=R, rotation=180, flipVertical=true\n- step 2: patternId=W, rotation=0, flipVertical=true\n- step 3: patternId=W, rotation=180, flipVertical=true\n- allowed patternId values for this task: R, W, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C013"} +{"sample_id": "C014", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N"], "observed_path_faces": [{"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C014_path_sequence.png"}, "metadata": {"level_id": 14, "name": "Reconstruct 014", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-014.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_right", "diamond", "arrow_left", "Y", "H", "arrow_right"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "arrow_right", "rotation": 90}, "BOTTOM": {"patternId": "arrow_right", "rotation": 270}, "FRONT": {"patternId": "diamond", "rotation": 180}, "BACK": {"patternId": "Y", "rotation": 0}, "LEFT": {"patternId": "H", "rotation": 180}, "RIGHT": {"patternId": "arrow_left", "rotation": 270}}, "bottom_faces": [{"patternId": "arrow_right", "rotation": 270, "x": 1, "y": 2}, {"patternId": "arrow_left", "rotation": 0, "x": 2, "y": 2}, {"patternId": "Y", "rotation": 90, "x": 2, "y": 1}], "slot_sequence": ["RIGHT", "BACK"], "required_slots": ["RIGHT", "BACK"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "Y", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "Y", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C014\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_left, rotation=0, flipVertical=true\n- step 2: patternId=Y, rotation=90, flipVertical=true\n- allowed patternId values for this task: arrow_left, Y, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C014"} +{"sample_id": "C015", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "N", "N"], "observed_path_faces": [{"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C015_path_sequence.png"}, "metadata": {"level_id": 15, "name": "Reconstruct 015", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-015.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["J", "4", "2", "6", "6", "O"], "start_x": 1, "start_y": 2, "grid_width": 3, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "J", "rotation": 180}, "BOTTOM": {"patternId": "O", "rotation": 90}, "FRONT": {"patternId": "4", "rotation": 90}, "BACK": {"patternId": "6", "rotation": 180}, "LEFT": {"patternId": "6", "rotation": 90}, "RIGHT": {"patternId": "2", "rotation": 0}}, "bottom_faces": [{"patternId": "O", "rotation": 90, "x": 1, "y": 2}, {"patternId": "4", "rotation": 90, "x": 1, "y": 3}, {"patternId": "O", "rotation": 90, "x": 1, "y": 2}, {"patternId": "6", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["FRONT", "BOTTOM", "BACK"], "required_slots": ["FRONT", "BOTTOM", "BACK"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "O", "rotation": 90}, "FRONT": {"patternId": "4", "rotation": 90}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "O", "rotation": 90}, "FRONT": {"patternId": "4", "rotation": 90}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C015\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): S -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=4, rotation=90, flipVertical=true\n- step 2: patternId=O, rotation=90, flipVertical=true\n- step 3: patternId=6, rotation=0, flipVertical=true\n- allowed patternId values for this task: 4, O, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C015"} +{"sample_id": "C016", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W"], "observed_path_faces": [{"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C016_path_sequence.png"}, "metadata": {"level_id": 16, "name": "Reconstruct 016", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-016.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["N", "H", "G", "triangle", "arrow_left", "smile"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "N", "rotation": 90}, "BOTTOM": {"patternId": "smile", "rotation": 180}, "FRONT": {"patternId": "H", "rotation": 180}, "BACK": {"patternId": "triangle", "rotation": 180}, "LEFT": {"patternId": "arrow_left", "rotation": 180}, "RIGHT": {"patternId": "G", "rotation": 0}}, "bottom_faces": [{"patternId": "smile", "rotation": 180, "x": 2, "y": 1}, {"patternId": "H", "rotation": 180, "x": 2, "y": 2}, {"patternId": "arrow_left", "rotation": 180, "x": 1, "y": 2}], "slot_sequence": ["FRONT", "LEFT"], "required_slots": ["FRONT", "LEFT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C016\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=H, rotation=180, flipVertical=true\n- step 2: patternId=arrow_left, rotation=180, flipVertical=true\n- allowed patternId values for this task: H, arrow_left, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C016"} +{"sample_id": "C017", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "W"], "observed_path_faces": [{"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C017_path_sequence.png"}, "metadata": {"level_id": 17, "name": "Reconstruct 017", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-017.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["A", "M", "M", "T", "D", "J"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "A", "rotation": 270}, "BOTTOM": {"patternId": "J", "rotation": 0}, "FRONT": {"patternId": "M", "rotation": 180}, "BACK": {"patternId": "T", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 90}}, "bottom_faces": [{"patternId": "J", "rotation": 0, "x": 1, "y": 2}, {"patternId": "M", "rotation": 180, "x": 2, "y": 2}, {"patternId": "T", "rotation": 90, "x": 2, "y": 1}, {"patternId": "J", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["RIGHT", "BACK", "BOTTOM"], "required_slots": ["RIGHT", "BACK", "BOTTOM"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "J", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "J", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C017\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=M, rotation=180, flipVertical=true\n- step 2: patternId=T, rotation=90, flipVertical=true\n- step 3: patternId=J, rotation=270, flipVertical=true\n- allowed patternId values for this task: M, T, J, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C017"} +{"sample_id": "C018", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "S"], "observed_path_faces": [{"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C018_path_sequence.png"}, "metadata": {"level_id": 18, "name": "Reconstruct 018", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-018.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["N", "triangle", "F", "smile", "9", "4"], "start_x": 2, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "N", "rotation": 90}, "BOTTOM": {"patternId": "4", "rotation": 0}, "FRONT": {"patternId": "triangle", "rotation": 0}, "BACK": {"patternId": "smile", "rotation": 0}, "LEFT": {"patternId": "9", "rotation": 90}, "RIGHT": {"patternId": "F", "rotation": 180}}, "bottom_faces": [{"patternId": "4", "rotation": 0, "x": 2, "y": 2}, {"patternId": "smile", "rotation": 180, "x": 2, "y": 1}, {"patternId": "9", "rotation": 270, "x": 1, "y": 1}, {"patternId": "4", "rotation": 270, "x": 1, "y": 2}], "slot_sequence": ["BACK", "LEFT", "BOTTOM"], "required_slots": ["BACK", "LEFT", "BOTTOM"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "4", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "smile", "rotation": 180}, "LEFT": {"patternId": "9", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "4", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "smile", "rotation": 180}, "LEFT": {"patternId": "9", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C018\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=smile, rotation=180, flipVertical=true\n- step 2: patternId=9, rotation=270, flipVertical=true\n- step 3: patternId=4, rotation=270, flipVertical=true\n- allowed patternId values for this task: smile, 9, 4, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C018"} +{"sample_id": "C019", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E"], "observed_path_faces": [{"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C019_path_sequence.png"}, "metadata": {"level_id": 19, "name": "Reconstruct 019", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-019.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["8", "5", "H", "square", "H", "Z"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 3, "true_solution_faces": {"TOP": {"patternId": "8", "rotation": 90}, "BOTTOM": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "5", "rotation": 180}, "BACK": {"patternId": "square", "rotation": 0}, "LEFT": {"patternId": "H", "rotation": 270}, "RIGHT": {"patternId": "H", "rotation": 0}}, "bottom_faces": [{"patternId": "Z", "rotation": 270, "x": 1, "y": 1}, {"patternId": "H", "rotation": 90, "x": 2, "y": 1}, {"patternId": "8", "rotation": 270, "x": 3, "y": 1}], "slot_sequence": ["RIGHT", "TOP"], "required_slots": ["RIGHT", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "8", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "H", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "8", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "H", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C019\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=H, rotation=90, flipVertical=true\n- step 2: patternId=8, rotation=270, flipVertical=true\n- allowed patternId values for this task: H, 8, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C019"} +{"sample_id": "C020", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N"], "observed_path_faces": [{"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C020_path_sequence.png"}, "metadata": {"level_id": 20, "name": "Reconstruct 020", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-020.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["B", "smile", "W", "9", "A", "S"], "start_x": 2, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "B", "rotation": 0}, "BOTTOM": {"patternId": "S", "rotation": 0}, "FRONT": {"patternId": "smile", "rotation": 180}, "BACK": {"patternId": "9", "rotation": 270}, "LEFT": {"patternId": "A", "rotation": 180}, "RIGHT": {"patternId": "W", "rotation": 0}}, "bottom_faces": [{"patternId": "S", "rotation": 0, "x": 2, "y": 2}, {"patternId": "A", "rotation": 90, "x": 1, "y": 2}, {"patternId": "9", "rotation": 180, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "BACK"], "required_slots": ["LEFT", "BACK"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "9", "rotation": 90}, "LEFT": {"patternId": "A", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "9", "rotation": 90}, "LEFT": {"patternId": "A", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C020\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=A, rotation=90, flipVertical=true\n- step 2: patternId=9, rotation=180, flipVertical=true\n- allowed patternId values for this task: A, 9, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C020"} +{"sample_id": "C021", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "S", "E"], "observed_path_faces": [{"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C021_path_sequence.png"}, "metadata": {"level_id": 21, "name": "Reconstruct 021", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-021.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["square", "circle", "N", "V", "circle", "4"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "square", "rotation": 270}, "BOTTOM": {"patternId": "4", "rotation": 270}, "FRONT": {"patternId": "circle", "rotation": 270}, "BACK": {"patternId": "V", "rotation": 90}, "LEFT": {"patternId": "circle", "rotation": 180}, "RIGHT": {"patternId": "N", "rotation": 180}}, "bottom_faces": [{"patternId": "4", "rotation": 270, "x": 1, "y": 2}, {"patternId": "V", "rotation": 270, "x": 1, "y": 1}, {"patternId": "4", "rotation": 270, "x": 1, "y": 2}, {"patternId": "N", "rotation": 270, "x": 2, "y": 2}], "slot_sequence": ["BACK", "BOTTOM", "RIGHT"], "required_slots": ["BACK", "BOTTOM", "RIGHT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "4", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "V", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "N", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "4", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "V", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "N", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C021\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): N -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=V, rotation=270, flipVertical=true\n- step 2: patternId=4, rotation=270, flipVertical=true\n- step 3: patternId=N, rotation=270, flipVertical=true\n- allowed patternId values for this task: V, 4, N, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C021"} +{"sample_id": "C022", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "E", "S"], "observed_path_faces": [{"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C022_path_sequence.png"}, "metadata": {"level_id": 22, "name": "Reconstruct 022", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-022.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["F", "W", "2", "G", "I", "W"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "F", "rotation": 270}, "BOTTOM": {"patternId": "W", "rotation": 180}, "FRONT": {"patternId": "W", "rotation": 180}, "BACK": {"patternId": "G", "rotation": 180}, "LEFT": {"patternId": "I", "rotation": 90}, "RIGHT": {"patternId": "2", "rotation": 90}}, "bottom_faces": [{"patternId": "W", "rotation": 180, "x": 2, "y": 1}, {"patternId": "I", "rotation": 0, "x": 1, "y": 1}, {"patternId": "W", "rotation": 180, "x": 2, "y": 1}, {"patternId": "W", "rotation": 180, "x": 2, "y": 2}], "slot_sequence": ["LEFT", "BOTTOM", "FRONT"], "required_slots": ["LEFT", "BOTTOM", "FRONT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 180}, "FRONT": {"patternId": "W", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "I", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 180}, "FRONT": {"patternId": "W", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "I", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C022\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): W -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=I, rotation=0, flipVertical=true\n- step 2: patternId=W, rotation=180, flipVertical=true\n- step 3: patternId=W, rotation=180, flipVertical=true\n- allowed patternId values for this task: I, W, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C022"} +{"sample_id": "C023", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N"], "observed_path_faces": [{"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C023_path_sequence.png"}, "metadata": {"level_id": 23, "name": "Reconstruct 023", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-023.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["C", "B", "T", "G", "4", "L"], "start_x": 1, "start_y": 3, "grid_width": 3, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "C", "rotation": 90}, "BOTTOM": {"patternId": "L", "rotation": 90}, "FRONT": {"patternId": "B", "rotation": 270}, "BACK": {"patternId": "G", "rotation": 180}, "LEFT": {"patternId": "4", "rotation": 0}, "RIGHT": {"patternId": "T", "rotation": 0}}, "bottom_faces": [{"patternId": "L", "rotation": 90, "x": 1, "y": 3}, {"patternId": "G", "rotation": 0, "x": 1, "y": 2}, {"patternId": "C", "rotation": 90, "x": 1, "y": 1}], "slot_sequence": ["BACK", "TOP"], "required_slots": ["BACK", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "C", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "G", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "C", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "G", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C023\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=G, rotation=0, flipVertical=true\n- step 2: patternId=C, rotation=90, flipVertical=true\n- allowed patternId values for this task: G, C, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C023"} +{"sample_id": "C024", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W"], "observed_path_faces": [{"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C024_path_sequence.png"}, "metadata": {"level_id": 24, "name": "Reconstruct 024", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-024.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["9", "1", "P", "A", "3", "smile"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "9", "rotation": 180}, "BOTTOM": {"patternId": "smile", "rotation": 180}, "FRONT": {"patternId": "1", "rotation": 180}, "BACK": {"patternId": "A", "rotation": 90}, "LEFT": {"patternId": "3", "rotation": 90}, "RIGHT": {"patternId": "P", "rotation": 0}}, "bottom_faces": [{"patternId": "smile", "rotation": 180, "x": 2, "y": 1}, {"patternId": "1", "rotation": 180, "x": 2, "y": 2}, {"patternId": "3", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["FRONT", "LEFT"], "required_slots": ["FRONT", "LEFT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "1", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "1", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C024\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=1, rotation=180, flipVertical=true\n- step 2: patternId=3, rotation=90, flipVertical=true\n- allowed patternId values for this task: 1, 3, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C024"} +{"sample_id": "C025", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E"], "observed_path_faces": [{"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C025_path_sequence.png"}, "metadata": {"level_id": 25, "name": "Reconstruct 025", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-025.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["9", "square", "arrow_right", "arrow_down", "2", "circle"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "9", "rotation": 270}, "BOTTOM": {"patternId": "circle", "rotation": 180}, "FRONT": {"patternId": "square", "rotation": 180}, "BACK": {"patternId": "arrow_down", "rotation": 0}, "LEFT": {"patternId": "2", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 90}}, "bottom_faces": [{"patternId": "circle", "rotation": 180, "x": 1, "y": 2}, {"patternId": "arrow_down", "rotation": 180, "x": 1, "y": 1}, {"patternId": "arrow_right", "rotation": 270, "x": 2, "y": 1}], "slot_sequence": ["BACK", "RIGHT"], "required_slots": ["BACK", "RIGHT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_down", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_down", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C025\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_down, rotation=180, flipVertical=true\n- step 2: patternId=arrow_right, rotation=270, flipVertical=true\n- allowed patternId values for this task: arrow_down, arrow_right, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C025"} +{"sample_id": "C026", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "S"], "observed_path_faces": [{"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C026_path_sequence.png"}, "metadata": {"level_id": 26, "name": "Reconstruct 026", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-026.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["square", "D", "K", "triangle", "R", "smile"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "square", "rotation": 90}, "BOTTOM": {"patternId": "smile", "rotation": 180}, "FRONT": {"patternId": "D", "rotation": 270}, "BACK": {"patternId": "triangle", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 0}, "RIGHT": {"patternId": "K", "rotation": 180}}, "bottom_faces": [{"patternId": "smile", "rotation": 180, "x": 2, "y": 1}, {"patternId": "R", "rotation": 270, "x": 1, "y": 1}, {"patternId": "D", "rotation": 180, "x": 1, "y": 2}, {"patternId": "K", "rotation": 90, "x": 1, "y": 3}], "slot_sequence": ["LEFT", "FRONT", "RIGHT"], "required_slots": ["LEFT", "FRONT", "RIGHT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 90}, "RIGHT": {"patternId": "K", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 90}, "RIGHT": {"patternId": "K", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C026\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=R, rotation=270, flipVertical=true\n- step 2: patternId=D, rotation=180, flipVertical=true\n- step 3: patternId=K, rotation=90, flipVertical=true\n- allowed patternId values for this task: R, D, K, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C026"} +{"sample_id": "C027", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "S", "N"], "observed_path_faces": [{"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C027_path_sequence.png"}, "metadata": {"level_id": 27, "name": "Reconstruct 027", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-027.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Y", "diamond", "G", "P", "D", "8"], "start_x": 1, "start_y": 2, "grid_width": 3, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "Y", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 270}, "FRONT": {"patternId": "diamond", "rotation": 90}, "BACK": {"patternId": "P", "rotation": 270}, "LEFT": {"patternId": "D", "rotation": 180}, "RIGHT": {"patternId": "G", "rotation": 270}}, "bottom_faces": [{"patternId": "8", "rotation": 270, "x": 1, "y": 2}, {"patternId": "P", "rotation": 90, "x": 1, "y": 1}, {"patternId": "8", "rotation": 270, "x": 1, "y": 2}, {"patternId": "P", "rotation": 90, "x": 1, "y": 1}], "slot_sequence": ["BACK", "BOTTOM", "BACK"], "required_slots": ["BACK", "BOTTOM"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "P", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "P", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C027\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): N -> S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=P, rotation=90, flipVertical=true\n- step 2: patternId=8, rotation=270, flipVertical=true\n- step 3: patternId=P, rotation=90, flipVertical=true\n- allowed patternId values for this task: P, 8, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C027"} +{"sample_id": "C028", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "N"], "observed_path_faces": [{"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C028_path_sequence.png"}, "metadata": {"level_id": 28, "name": "Reconstruct 028", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-028.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["9", "circle", "6", "M", "P", "star"], "start_x": 1, "start_y": 1, "grid_width": 3, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "9", "rotation": 0}, "BOTTOM": {"patternId": "star", "rotation": 90}, "FRONT": {"patternId": "circle", "rotation": 270}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "P", "rotation": 270}, "RIGHT": {"patternId": "6", "rotation": 90}}, "bottom_faces": [{"patternId": "star", "rotation": 90, "x": 1, "y": 1}, {"patternId": "circle", "rotation": 270, "x": 1, "y": 2}, {"patternId": "star", "rotation": 90, "x": 1, "y": 1}], "slot_sequence": ["FRONT", "BOTTOM"], "required_slots": ["FRONT", "BOTTOM"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "star", "rotation": 90}, "FRONT": {"patternId": "circle", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "star", "rotation": 90}, "FRONT": {"patternId": "circle", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C028\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=circle, rotation=270, flipVertical=true\n- step 2: patternId=star, rotation=90, flipVertical=true\n- allowed patternId values for this task: circle, star, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C028"} +{"sample_id": "C029", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "N"], "observed_path_faces": [{"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C029_path_sequence.png"}, "metadata": {"level_id": 29, "name": "Reconstruct 029", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-029.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["S", "P", "arrow_right", "S", "A", "E"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "S", "rotation": 270}, "BOTTOM": {"patternId": "E", "rotation": 0}, "FRONT": {"patternId": "P", "rotation": 270}, "BACK": {"patternId": "S", "rotation": 90}, "LEFT": {"patternId": "A", "rotation": 90}, "RIGHT": {"patternId": "arrow_right", "rotation": 0}}, "bottom_faces": [{"patternId": "E", "rotation": 0, "x": 2, "y": 1}, {"patternId": "A", "rotation": 0, "x": 1, "y": 1}, {"patternId": "P", "rotation": 180, "x": 1, "y": 2}, {"patternId": "A", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "FRONT", "LEFT"], "required_slots": ["LEFT", "FRONT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "P", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "A", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "P", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "A", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C029\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=A, rotation=0, flipVertical=true\n- step 2: patternId=P, rotation=180, flipVertical=true\n- step 3: patternId=A, rotation=0, flipVertical=true\n- allowed patternId values for this task: A, P, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C029"} +{"sample_id": "C030", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "W"], "observed_path_faces": [{"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C030_path_sequence.png"}, "metadata": {"level_id": 30, "name": "Reconstruct 030", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-030.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["smile", "N", "B", "H", "R", "I"], "start_x": 3, "start_y": 2, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "smile", "rotation": 0}, "BOTTOM": {"patternId": "I", "rotation": 90}, "FRONT": {"patternId": "N", "rotation": 90}, "BACK": {"patternId": "H", "rotation": 270}, "LEFT": {"patternId": "R", "rotation": 0}, "RIGHT": {"patternId": "B", "rotation": 90}}, "bottom_faces": [{"patternId": "I", "rotation": 90, "x": 3, "y": 2}, {"patternId": "H", "rotation": 90, "x": 3, "y": 1}, {"patternId": "R", "rotation": 180, "x": 2, "y": 1}, {"patternId": "N", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["BACK", "LEFT", "FRONT"], "required_slots": ["BACK", "LEFT", "FRONT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 90}, "BACK": {"patternId": "H", "rotation": 90}, "LEFT": {"patternId": "R", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 90}, "BACK": {"patternId": "H", "rotation": 90}, "LEFT": {"patternId": "R", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C030\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=H, rotation=90, flipVertical=true\n- step 2: patternId=R, rotation=180, flipVertical=true\n- step 3: patternId=N, rotation=270, flipVertical=true\n- allowed patternId values for this task: H, R, N, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C030"} +{"sample_id": "C031", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N"], "observed_path_faces": [{"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C031_path_sequence.png"}, "metadata": {"level_id": 31, "name": "Reconstruct 031", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-031.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["C", "W", "star", "T", "G", "N"], "start_x": 2, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "C", "rotation": 90}, "BOTTOM": {"patternId": "N", "rotation": 90}, "FRONT": {"patternId": "W", "rotation": 270}, "BACK": {"patternId": "T", "rotation": 90}, "LEFT": {"patternId": "G", "rotation": 0}, "RIGHT": {"patternId": "star", "rotation": 270}}, "bottom_faces": [{"patternId": "N", "rotation": 90, "x": 2, "y": 2}, {"patternId": "G", "rotation": 270, "x": 1, "y": 2}, {"patternId": "T", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "BACK"], "required_slots": ["LEFT", "BACK"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 270}, "LEFT": {"patternId": "G", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 270}, "LEFT": {"patternId": "G", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C031\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=G, rotation=270, flipVertical=true\n- step 2: patternId=T, rotation=0, flipVertical=true\n- allowed patternId values for this task: G, T, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C031"} +{"sample_id": "C032", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "N"], "observed_path_faces": [{"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C032_path_sequence.png"}, "metadata": {"level_id": 32, "name": "Reconstruct 032", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-032.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["9", "6", "7", "W", "M", "X"], "start_x": 1, "start_y": 1, "grid_width": 3, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "9", "rotation": 90}, "BOTTOM": {"patternId": "X", "rotation": 90}, "FRONT": {"patternId": "6", "rotation": 90}, "BACK": {"patternId": "W", "rotation": 270}, "LEFT": {"patternId": "M", "rotation": 270}, "RIGHT": {"patternId": "7", "rotation": 270}}, "bottom_faces": [{"patternId": "X", "rotation": 90, "x": 1, "y": 1}, {"patternId": "6", "rotation": 90, "x": 1, "y": 2}, {"patternId": "9", "rotation": 90, "x": 1, "y": 3}, {"patternId": "6", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["FRONT", "TOP", "FRONT"], "required_slots": ["FRONT", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "9", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "6", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "9", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "6", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C032\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=6, rotation=90, flipVertical=true\n- step 2: patternId=9, rotation=90, flipVertical=true\n- step 3: patternId=6, rotation=90, flipVertical=true\n- allowed patternId values for this task: 6, 9, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C032"} +{"sample_id": "C033", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "N"], "observed_path_faces": [{"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C033_path_sequence.png"}, "metadata": {"level_id": 33, "name": "Reconstruct 033", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-033.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["5", "X", "3", "K", "I", "E"], "start_x": 2, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "5", "rotation": 270}, "BOTTOM": {"patternId": "E", "rotation": 270}, "FRONT": {"patternId": "X", "rotation": 180}, "BACK": {"patternId": "K", "rotation": 90}, "LEFT": {"patternId": "I", "rotation": 0}, "RIGHT": {"patternId": "3", "rotation": 270}}, "bottom_faces": [{"patternId": "E", "rotation": 270, "x": 2, "y": 3}, {"patternId": "K", "rotation": 270, "x": 2, "y": 2}, {"patternId": "I", "rotation": 180, "x": 1, "y": 2}, {"patternId": "5", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["BACK", "LEFT", "TOP"], "required_slots": ["BACK", "LEFT", "TOP"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "5", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "I", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "5", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "I", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C033\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=K, rotation=270, flipVertical=true\n- step 2: patternId=I, rotation=180, flipVertical=true\n- step 3: patternId=5, rotation=0, flipVertical=true\n- allowed patternId values for this task: K, I, 5, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C033"} +{"sample_id": "C034", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W"], "observed_path_faces": [{"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C034_path_sequence.png"}, "metadata": {"level_id": 34, "name": "Reconstruct 034", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-034.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["U", "P", "circle", "V", "H", "diamond"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 3, "true_solution_faces": {"TOP": {"patternId": "U", "rotation": 0}, "BOTTOM": {"patternId": "diamond", "rotation": 270}, "FRONT": {"patternId": "P", "rotation": 270}, "BACK": {"patternId": "V", "rotation": 90}, "LEFT": {"patternId": "H", "rotation": 270}, "RIGHT": {"patternId": "circle", "rotation": 180}}, "bottom_faces": [{"patternId": "diamond", "rotation": 270, "x": 3, "y": 1}, {"patternId": "H", "rotation": 180, "x": 2, "y": 1}, {"patternId": "U", "rotation": 180, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "TOP"], "required_slots": ["LEFT", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "U", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "H", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "U", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "H", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C034\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=H, rotation=180, flipVertical=true\n- step 2: patternId=U, rotation=180, flipVertical=true\n- allowed patternId values for this task: H, U, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C034"} +{"sample_id": "C035", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S"], "observed_path_faces": [{"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C035_path_sequence.png"}, "metadata": {"level_id": 35, "name": "Reconstruct 035", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-035.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_right", "arrow_left", "K", "circle", "Z", "heart"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "arrow_right", "rotation": 180}, "BOTTOM": {"patternId": "heart", "rotation": 270}, "FRONT": {"patternId": "arrow_left", "rotation": 180}, "BACK": {"patternId": "circle", "rotation": 0}, "LEFT": {"patternId": "Z", "rotation": 270}, "RIGHT": {"patternId": "K", "rotation": 0}}, "bottom_faces": [{"patternId": "heart", "rotation": 270, "x": 2, "y": 1}, {"patternId": "Z", "rotation": 180, "x": 1, "y": 1}, {"patternId": "arrow_left", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["LEFT", "FRONT"], "required_slots": ["LEFT", "FRONT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Z", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Z", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C035\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Z, rotation=180, flipVertical=true\n- step 2: patternId=arrow_left, rotation=90, flipVertical=true\n- allowed patternId values for this task: Z, arrow_left, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C035"} +{"sample_id": "C036", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "S"], "observed_path_faces": [{"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C036_path_sequence.png"}, "metadata": {"level_id": 36, "name": "Reconstruct 036", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-036.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["smile", "3", "G", "arrow_up", "circle", "smile"], "start_x": 2, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "smile", "rotation": 270}, "BOTTOM": {"patternId": "smile", "rotation": 90}, "FRONT": {"patternId": "3", "rotation": 90}, "BACK": {"patternId": "arrow_up", "rotation": 270}, "LEFT": {"patternId": "circle", "rotation": 90}, "RIGHT": {"patternId": "G", "rotation": 270}}, "bottom_faces": [{"patternId": "smile", "rotation": 90, "x": 2, "y": 2}, {"patternId": "circle", "rotation": 0, "x": 1, "y": 2}, {"patternId": "arrow_up", "rotation": 180, "x": 1, "y": 1}, {"patternId": "circle", "rotation": 0, "x": 1, "y": 2}], "slot_sequence": ["LEFT", "BACK", "LEFT"], "required_slots": ["LEFT", "BACK"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_up", "rotation": 90}, "LEFT": {"patternId": "circle", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_up", "rotation": 90}, "LEFT": {"patternId": "circle", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C036\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=circle, rotation=0, flipVertical=true\n- step 2: patternId=arrow_up, rotation=180, flipVertical=true\n- step 3: patternId=circle, rotation=0, flipVertical=true\n- allowed patternId values for this task: circle, arrow_up, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C036"} +{"sample_id": "C037", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W"], "observed_path_faces": [{"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C037_path_sequence.png"}, "metadata": {"level_id": 37, "name": "Reconstruct 037", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-037.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["3", "B", "N", "H", "2", "5"], "start_x": 2, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "3", "rotation": 270}, "BOTTOM": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "B", "rotation": 90}, "BACK": {"patternId": "H", "rotation": 90}, "LEFT": {"patternId": "2", "rotation": 180}, "RIGHT": {"patternId": "N", "rotation": 0}}, "bottom_faces": [{"patternId": "5", "rotation": 90, "x": 2, "y": 2}, {"patternId": "H", "rotation": 270, "x": 2, "y": 1}, {"patternId": "2", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["BACK", "LEFT"], "required_slots": ["BACK", "LEFT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "H", "rotation": 270}, "LEFT": {"patternId": "2", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "H", "rotation": 270}, "LEFT": {"patternId": "2", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C037\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=H, rotation=270, flipVertical=true\n- step 2: patternId=2, rotation=0, flipVertical=true\n- allowed patternId values for this task: H, 2, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C037"} +{"sample_id": "C038", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E"], "observed_path_faces": [{"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C038_path_sequence.png"}, "metadata": {"level_id": 38, "name": "Reconstruct 038", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-038.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["A", "H", "P", "Q", "N", "smile"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "A", "rotation": 180}, "BOTTOM": {"patternId": "smile", "rotation": 180}, "FRONT": {"patternId": "H", "rotation": 270}, "BACK": {"patternId": "Q", "rotation": 90}, "LEFT": {"patternId": "N", "rotation": 270}, "RIGHT": {"patternId": "P", "rotation": 0}}, "bottom_faces": [{"patternId": "smile", "rotation": 180, "x": 1, "y": 2}, {"patternId": "Q", "rotation": 270, "x": 1, "y": 1}, {"patternId": "P", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["BACK", "RIGHT"], "required_slots": ["BACK", "RIGHT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "Q", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "P", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "Q", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "P", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C038\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Q, rotation=270, flipVertical=true\n- step 2: patternId=P, rotation=180, flipVertical=true\n- allowed patternId values for this task: Q, P, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C038"} +{"sample_id": "C039", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N"], "observed_path_faces": [{"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C039_path_sequence.png"}, "metadata": {"level_id": 39, "name": "Reconstruct 039", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-039.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["G", "E", "5", "B", "I", "Z"], "start_x": 2, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "G", "rotation": 270}, "BOTTOM": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "E", "rotation": 180}, "BACK": {"patternId": "B", "rotation": 180}, "LEFT": {"patternId": "I", "rotation": 90}, "RIGHT": {"patternId": "5", "rotation": 90}}, "bottom_faces": [{"patternId": "Z", "rotation": 270, "x": 2, "y": 2}, {"patternId": "I", "rotation": 0, "x": 1, "y": 2}, {"patternId": "B", "rotation": 90, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "BACK"], "required_slots": ["LEFT", "BACK"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "I", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "I", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C039\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=I, rotation=0, flipVertical=true\n- step 2: patternId=B, rotation=90, flipVertical=true\n- allowed patternId values for this task: I, B, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C039"} +{"sample_id": "C040", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W"], "observed_path_faces": [{"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C040_path_sequence.png"}, "metadata": {"level_id": 40, "name": "Reconstruct 040", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-040.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["heart", "W", "1", "I", "smile", "I"], "start_x": 2, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "heart", "rotation": 180}, "BOTTOM": {"patternId": "I", "rotation": 180}, "FRONT": {"patternId": "W", "rotation": 270}, "BACK": {"patternId": "I", "rotation": 180}, "LEFT": {"patternId": "smile", "rotation": 180}, "RIGHT": {"patternId": "1", "rotation": 270}}, "bottom_faces": [{"patternId": "I", "rotation": 180, "x": 2, "y": 2}, {"patternId": "I", "rotation": 0, "x": 2, "y": 1}, {"patternId": "smile", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["BACK", "LEFT"], "required_slots": ["BACK", "LEFT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 0}, "LEFT": {"patternId": "smile", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 0}, "LEFT": {"patternId": "smile", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C040\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=I, rotation=0, flipVertical=true\n- step 2: patternId=smile, rotation=0, flipVertical=true\n- allowed patternId values for this task: I, smile, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C040"} +{"sample_id": "C041", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S"], "observed_path_faces": [{"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C041_path_sequence.png"}, "metadata": {"level_id": 41, "name": "Reconstruct 041", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-041.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["6", "star", "6", "N", "E", "Y"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "6", "rotation": 270}, "BOTTOM": {"patternId": "Y", "rotation": 270}, "FRONT": {"patternId": "star", "rotation": 0}, "BACK": {"patternId": "N", "rotation": 90}, "LEFT": {"patternId": "E", "rotation": 180}, "RIGHT": {"patternId": "6", "rotation": 270}}, "bottom_faces": [{"patternId": "Y", "rotation": 270, "x": 1, "y": 1}, {"patternId": "6", "rotation": 0, "x": 2, "y": 1}, {"patternId": "star", "rotation": 90, "x": 2, "y": 2}], "slot_sequence": ["RIGHT", "FRONT"], "required_slots": ["RIGHT", "FRONT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C041\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=6, rotation=0, flipVertical=true\n- step 2: patternId=star, rotation=90, flipVertical=true\n- allowed patternId values for this task: 6, star, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C041"} +{"sample_id": "C042", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W"], "observed_path_faces": [{"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C042_path_sequence.png"}, "metadata": {"level_id": 42, "name": "Reconstruct 042", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-042.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["K", "arrow_left", "K", "R", "star", "M"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "K", "rotation": 270}, "BOTTOM": {"patternId": "M", "rotation": 180}, "FRONT": {"patternId": "arrow_left", "rotation": 90}, "BACK": {"patternId": "R", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 270}, "RIGHT": {"patternId": "K", "rotation": 270}}, "bottom_faces": [{"patternId": "M", "rotation": 180, "x": 2, "y": 1}, {"patternId": "arrow_left", "rotation": 90, "x": 2, "y": 2}, {"patternId": "star", "rotation": 270, "x": 1, "y": 2}], "slot_sequence": ["FRONT", "LEFT"], "required_slots": ["FRONT", "LEFT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C042\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_left, rotation=90, flipVertical=true\n- step 2: patternId=star, rotation=270, flipVertical=true\n- allowed patternId values for this task: arrow_left, star, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C042"} +{"sample_id": "C043", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E"], "observed_path_faces": [{"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C043_path_sequence.png"}, "metadata": {"level_id": 43, "name": "Reconstruct 043", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-043.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["2", "9", "S", "P", "Y", "D"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "2", "rotation": 90}, "BOTTOM": {"patternId": "D", "rotation": 270}, "FRONT": {"patternId": "9", "rotation": 0}, "BACK": {"patternId": "P", "rotation": 90}, "LEFT": {"patternId": "Y", "rotation": 180}, "RIGHT": {"patternId": "S", "rotation": 90}}, "bottom_faces": [{"patternId": "D", "rotation": 270, "x": 1, "y": 2}, {"patternId": "P", "rotation": 270, "x": 1, "y": 1}, {"patternId": "S", "rotation": 270, "x": 2, "y": 1}], "slot_sequence": ["BACK", "RIGHT"], "required_slots": ["BACK", "RIGHT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "P", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "P", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C043\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=P, rotation=270, flipVertical=true\n- step 2: patternId=S, rotation=270, flipVertical=true\n- allowed patternId values for this task: P, S, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C043"} +{"sample_id": "C044", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "W"], "observed_path_faces": [{"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C044_path_sequence.png"}, "metadata": {"level_id": 44, "name": "Reconstruct 044", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-044.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["heart", "arrow_up", "7", "1", "smile", "heart"], "start_x": 4, "start_y": 1, "grid_width": 6, "grid_height": 3, "true_solution_faces": {"TOP": {"patternId": "heart", "rotation": 0}, "BOTTOM": {"patternId": "heart", "rotation": 90}, "FRONT": {"patternId": "arrow_up", "rotation": 0}, "BACK": {"patternId": "1", "rotation": 90}, "LEFT": {"patternId": "smile", "rotation": 270}, "RIGHT": {"patternId": "7", "rotation": 270}}, "bottom_faces": [{"patternId": "heart", "rotation": 90, "x": 4, "y": 1}, {"patternId": "smile", "rotation": 180, "x": 3, "y": 1}, {"patternId": "heart", "rotation": 180, "x": 2, "y": 1}, {"patternId": "7", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "TOP", "RIGHT"], "required_slots": ["LEFT", "TOP", "RIGHT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "heart", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "smile", "rotation": 0}, "RIGHT": {"patternId": "7", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "heart", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "smile", "rotation": 0}, "RIGHT": {"patternId": "7", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C044\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=smile, rotation=180, flipVertical=true\n- step 2: patternId=heart, rotation=180, flipVertical=true\n- step 3: patternId=7, rotation=0, flipVertical=true\n- allowed patternId values for this task: smile, heart, 7, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C044"} +{"sample_id": "C045", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "E"], "observed_path_faces": [{"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C045_path_sequence.png"}, "metadata": {"level_id": 45, "name": "Reconstruct 045", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-045.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["circle", "R", "U", "D", "7", "P"], "start_x": 1, "start_y": 2, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "circle", "rotation": 270}, "BOTTOM": {"patternId": "P", "rotation": 270}, "FRONT": {"patternId": "R", "rotation": 180}, "BACK": {"patternId": "D", "rotation": 180}, "LEFT": {"patternId": "7", "rotation": 90}, "RIGHT": {"patternId": "U", "rotation": 180}}, "bottom_faces": [{"patternId": "P", "rotation": 270, "x": 1, "y": 2}, {"patternId": "U", "rotation": 270, "x": 2, "y": 2}, {"patternId": "D", "rotation": 270, "x": 2, "y": 1}, {"patternId": "circle", "rotation": 180, "x": 3, "y": 1}], "slot_sequence": ["RIGHT", "BACK", "TOP"], "required_slots": ["RIGHT", "BACK", "TOP"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "circle", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "U", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "U", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C045\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=U, rotation=270, flipVertical=true\n- step 2: patternId=D, rotation=270, flipVertical=true\n- step 3: patternId=circle, rotation=180, flipVertical=true\n- allowed patternId values for this task: U, D, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C045"} +{"sample_id": "C046", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "E"], "observed_path_faces": [{"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C046_path_sequence.png"}, "metadata": {"level_id": 46, "name": "Reconstruct 046", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-046.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_left", "W", "arrow_up", "6", "C", "I"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 3, "true_solution_faces": {"TOP": {"patternId": "arrow_left", "rotation": 90}, "BOTTOM": {"patternId": "I", "rotation": 0}, "FRONT": {"patternId": "W", "rotation": 180}, "BACK": {"patternId": "6", "rotation": 270}, "LEFT": {"patternId": "C", "rotation": 90}, "RIGHT": {"patternId": "arrow_up", "rotation": 180}}, "bottom_faces": [{"patternId": "I", "rotation": 0, "x": 3, "y": 1}, {"patternId": "C", "rotation": 0, "x": 2, "y": 1}, {"patternId": "arrow_left", "rotation": 270, "x": 1, "y": 1}, {"patternId": "C", "rotation": 0, "x": 2, "y": 1}], "slot_sequence": ["LEFT", "TOP", "LEFT"], "required_slots": ["LEFT", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "arrow_left", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "C", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "arrow_left", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "C", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C046\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=C, rotation=0, flipVertical=true\n- step 2: patternId=arrow_left, rotation=270, flipVertical=true\n- step 3: patternId=C, rotation=0, flipVertical=true\n- allowed patternId values for this task: C, arrow_left, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C046"} +{"sample_id": "C047", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "N"], "observed_path_faces": [{"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C047_path_sequence.png"}, "metadata": {"level_id": 47, "name": "Reconstruct 047", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-047.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["N", "heart", "B", "arrow_up", "H", "L"], "start_x": 3, "start_y": 2, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "N", "rotation": 0}, "BOTTOM": {"patternId": "L", "rotation": 180}, "FRONT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "arrow_up", "rotation": 270}, "LEFT": {"patternId": "H", "rotation": 90}, "RIGHT": {"patternId": "B", "rotation": 270}}, "bottom_faces": [{"patternId": "L", "rotation": 180, "x": 3, "y": 2}, {"patternId": "H", "rotation": 0, "x": 2, "y": 2}, {"patternId": "N", "rotation": 180, "x": 1, "y": 2}, {"patternId": "arrow_up", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "TOP", "BACK"], "required_slots": ["LEFT", "TOP", "BACK"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "N", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_up", "rotation": 90}, "LEFT": {"patternId": "H", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "N", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_up", "rotation": 90}, "LEFT": {"patternId": "H", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C047\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=H, rotation=0, flipVertical=true\n- step 2: patternId=N, rotation=180, flipVertical=true\n- step 3: patternId=arrow_up, rotation=270, flipVertical=true\n- allowed patternId values for this task: H, N, arrow_up, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C047"} +{"sample_id": "C048", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "W"], "observed_path_faces": [{"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C048_path_sequence.png"}, "metadata": {"level_id": 48, "name": "Reconstruct 048", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-048.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_left", "smile", "arrow_up", "plus", "A", "smile"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "arrow_left", "rotation": 0}, "BOTTOM": {"patternId": "smile", "rotation": 180}, "FRONT": {"patternId": "smile", "rotation": 180}, "BACK": {"patternId": "plus", "rotation": 90}, "LEFT": {"patternId": "A", "rotation": 270}, "RIGHT": {"patternId": "arrow_up", "rotation": 180}}, "bottom_faces": [{"patternId": "smile", "rotation": 180, "x": 3, "y": 1}, {"patternId": "smile", "rotation": 180, "x": 3, "y": 2}, {"patternId": "A", "rotation": 270, "x": 2, "y": 2}, {"patternId": "plus", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["FRONT", "LEFT", "BACK"], "required_slots": ["FRONT", "LEFT", "BACK"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "smile", "rotation": 180}, "BACK": {"patternId": "plus", "rotation": 270}, "LEFT": {"patternId": "A", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "smile", "rotation": 180}, "BACK": {"patternId": "plus", "rotation": 270}, "LEFT": {"patternId": "A", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C048\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=smile, rotation=180, flipVertical=true\n- step 2: patternId=A, rotation=270, flipVertical=true\n- step 3: patternId=plus, rotation=90, flipVertical=true\n- allowed patternId values for this task: smile, A, plus, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C048"} +{"sample_id": "C049", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "E"], "observed_path_faces": [{"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C049_path_sequence.png"}, "metadata": {"level_id": 49, "name": "Reconstruct 049", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-049.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["V", "D", "Y", "arrow_left", "Z", "V"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "V", "rotation": 180}, "BOTTOM": {"patternId": "V", "rotation": 270}, "FRONT": {"patternId": "D", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 90}, "LEFT": {"patternId": "Z", "rotation": 90}, "RIGHT": {"patternId": "Y", "rotation": 270}}, "bottom_faces": [{"patternId": "V", "rotation": 270, "x": 1, "y": 1}, {"patternId": "D", "rotation": 0, "x": 1, "y": 2}, {"patternId": "V", "rotation": 180, "x": 1, "y": 3}, {"patternId": "Y", "rotation": 180, "x": 2, "y": 3}], "slot_sequence": ["FRONT", "TOP", "RIGHT"], "required_slots": ["FRONT", "TOP", "RIGHT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "V", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Y", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "V", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Y", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C049\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=D, rotation=0, flipVertical=true\n- step 2: patternId=V, rotation=180, flipVertical=true\n- step 3: patternId=Y, rotation=180, flipVertical=true\n- allowed patternId values for this task: D, V, Y, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C049"} +{"sample_id": "C050", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "E", "N"], "observed_path_faces": [{"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C050_path_sequence.png"}, "metadata": {"level_id": 50, "name": "Reconstruct 050", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-050.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["smile", "T", "square", "3", "P", "8"], "start_x": 2, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "smile", "rotation": 90}, "BOTTOM": {"patternId": "8", "rotation": 0}, "FRONT": {"patternId": "T", "rotation": 180}, "BACK": {"patternId": "3", "rotation": 0}, "LEFT": {"patternId": "P", "rotation": 270}, "RIGHT": {"patternId": "square", "rotation": 90}}, "bottom_faces": [{"patternId": "8", "rotation": 0, "x": 2, "y": 2}, {"patternId": "P", "rotation": 180, "x": 1, "y": 2}, {"patternId": "8", "rotation": 0, "x": 2, "y": 2}, {"patternId": "3", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["LEFT", "BOTTOM", "BACK"], "required_slots": ["LEFT", "BOTTOM", "BACK"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "3", "rotation": 180}, "LEFT": {"patternId": "P", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "3", "rotation": 180}, "LEFT": {"patternId": "P", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C050\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): W -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=P, rotation=180, flipVertical=true\n- step 2: patternId=8, rotation=0, flipVertical=true\n- step 3: patternId=3, rotation=180, flipVertical=true\n- allowed patternId values for this task: P, 8, 3, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C050"} +{"sample_id": "C051", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "W"], "observed_path_faces": [{"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C051_path_sequence.png"}, "metadata": {"level_id": 51, "name": "Reconstruct 051", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-051.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["6", "plus", "L", "plus", "star", "C"], "start_x": 4, "start_y": 1, "grid_width": 6, "grid_height": 3, "true_solution_faces": {"TOP": {"patternId": "6", "rotation": 0}, "BOTTOM": {"patternId": "C", "rotation": 270}, "FRONT": {"patternId": "plus", "rotation": 270}, "BACK": {"patternId": "plus", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 180}, "RIGHT": {"patternId": "L", "rotation": 180}}, "bottom_faces": [{"patternId": "C", "rotation": 270, "x": 4, "y": 1}, {"patternId": "star", "rotation": 90, "x": 3, "y": 1}, {"patternId": "6", "rotation": 180, "x": 2, "y": 1}, {"patternId": "L", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "TOP", "RIGHT"], "required_slots": ["LEFT", "TOP", "RIGHT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "6", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 270}, "RIGHT": {"patternId": "L", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 270}, "RIGHT": {"patternId": "L", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C051\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=star, rotation=90, flipVertical=true\n- step 2: patternId=6, rotation=180, flipVertical=true\n- step 3: patternId=L, rotation=270, flipVertical=true\n- allowed patternId values for this task: star, 6, L, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C051"} +{"sample_id": "C052", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "W"], "observed_path_faces": [{"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C052_path_sequence.png"}, "metadata": {"level_id": 52, "name": "Reconstruct 052", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-052.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["square", "arrow_down", "P", "W", "U", "square"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "square", "rotation": 180}, "BOTTOM": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "arrow_down", "rotation": 90}, "BACK": {"patternId": "W", "rotation": 180}, "LEFT": {"patternId": "U", "rotation": 90}, "RIGHT": {"patternId": "P", "rotation": 90}}, "bottom_faces": [{"patternId": "square", "rotation": 90, "x": 1, "y": 1}, {"patternId": "arrow_down", "rotation": 90, "x": 1, "y": 2}, {"patternId": "P", "rotation": 90, "x": 2, "y": 2}, {"patternId": "arrow_down", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["FRONT", "RIGHT", "FRONT"], "required_slots": ["FRONT", "RIGHT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_down", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "P", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_down", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "P", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C052\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_down, rotation=90, flipVertical=true\n- step 2: patternId=P, rotation=90, flipVertical=true\n- step 3: patternId=arrow_down, rotation=90, flipVertical=true\n- allowed patternId values for this task: arrow_down, P, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C052"} +{"sample_id": "C053", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S"], "observed_path_faces": [{"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C053_path_sequence.png"}, "metadata": {"level_id": 53, "name": "Reconstruct 053", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-053.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["9", "heart", "arrow_right", "9", "L", "C"], "start_x": 1, "start_y": 1, "grid_width": 3, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "9", "rotation": 0}, "BOTTOM": {"patternId": "C", "rotation": 270}, "FRONT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "9", "rotation": 180}, "LEFT": {"patternId": "L", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}}, "bottom_faces": [{"patternId": "C", "rotation": 270, "x": 1, "y": 1}, {"patternId": "heart", "rotation": 270, "x": 1, "y": 2}, {"patternId": "9", "rotation": 0, "x": 1, "y": 3}], "slot_sequence": ["FRONT", "TOP"], "required_slots": ["FRONT", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "9", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "9", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C053\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=heart, rotation=270, flipVertical=true\n- step 2: patternId=9, rotation=0, flipVertical=true\n- allowed patternId values for this task: heart, 9, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C053"} +{"sample_id": "C054", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "S"], "observed_path_faces": [{"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C054_path_sequence.png"}, "metadata": {"level_id": 54, "name": "Reconstruct 054", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-054.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["M", "U", "star", "M", "5", "3"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "M", "rotation": 0}, "BOTTOM": {"patternId": "3", "rotation": 270}, "FRONT": {"patternId": "U", "rotation": 180}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "5", "rotation": 180}, "RIGHT": {"patternId": "star", "rotation": 0}}, "bottom_faces": [{"patternId": "3", "rotation": 270, "x": 2, "y": 1}, {"patternId": "U", "rotation": 180, "x": 2, "y": 2}, {"patternId": "5", "rotation": 180, "x": 1, "y": 2}, {"patternId": "M", "rotation": 270, "x": 1, "y": 3}], "slot_sequence": ["FRONT", "LEFT", "TOP"], "required_slots": ["FRONT", "LEFT", "TOP"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "M", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "U", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "5", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "U", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "5", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C054\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=U, rotation=180, flipVertical=true\n- step 2: patternId=5, rotation=180, flipVertical=true\n- step 3: patternId=M, rotation=270, flipVertical=true\n- allowed patternId values for this task: U, 5, M, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C054"} +{"sample_id": "C055", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "N"], "observed_path_faces": [{"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C055_path_sequence.png"}, "metadata": {"level_id": 55, "name": "Reconstruct 055", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-055.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["7", "E", "K", "9", "9", "heart"], "start_x": 2, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "7", "rotation": 180}, "BOTTOM": {"patternId": "heart", "rotation": 270}, "FRONT": {"patternId": "E", "rotation": 90}, "BACK": {"patternId": "9", "rotation": 270}, "LEFT": {"patternId": "9", "rotation": 90}, "RIGHT": {"patternId": "K", "rotation": 270}}, "bottom_faces": [{"patternId": "heart", "rotation": 270, "x": 2, "y": 3}, {"patternId": "9", "rotation": 0, "x": 1, "y": 3}, {"patternId": "9", "rotation": 180, "x": 1, "y": 2}, {"patternId": "K", "rotation": 180, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "BACK", "RIGHT"], "required_slots": ["LEFT", "BACK", "RIGHT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "9", "rotation": 90}, "LEFT": {"patternId": "9", "rotation": 180}, "RIGHT": {"patternId": "K", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "9", "rotation": 90}, "LEFT": {"patternId": "9", "rotation": 180}, "RIGHT": {"patternId": "K", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C055\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=9, rotation=0, flipVertical=true\n- step 2: patternId=9, rotation=180, flipVertical=true\n- step 3: patternId=K, rotation=180, flipVertical=true\n- allowed patternId values for this task: 9, K, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C055"} +{"sample_id": "C056", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E"], "observed_path_faces": [{"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C056_path_sequence.png"}, "metadata": {"level_id": 56, "name": "Reconstruct 056", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-056.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["square", "arrow_left", "J", "star", "square", "6"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "square", "rotation": 270}, "BOTTOM": {"patternId": "6", "rotation": 270}, "FRONT": {"patternId": "arrow_left", "rotation": 180}, "BACK": {"patternId": "star", "rotation": 0}, "LEFT": {"patternId": "square", "rotation": 90}, "RIGHT": {"patternId": "J", "rotation": 90}}, "bottom_faces": [{"patternId": "6", "rotation": 270, "x": 1, "y": 2}, {"patternId": "star", "rotation": 180, "x": 1, "y": 1}, {"patternId": "J", "rotation": 270, "x": 2, "y": 1}], "slot_sequence": ["BACK", "RIGHT"], "required_slots": ["BACK", "RIGHT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "J", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "J", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C056\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=star, rotation=180, flipVertical=true\n- step 2: patternId=J, rotation=270, flipVertical=true\n- allowed patternId values for this task: star, J, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C056"} +{"sample_id": "C057", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "W"], "observed_path_faces": [{"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C057_path_sequence.png"}, "metadata": {"level_id": 57, "name": "Reconstruct 057", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-057.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["4", "7", "J", "plus", "arrow_left", "R"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "4", "rotation": 270}, "BOTTOM": {"patternId": "R", "rotation": 180}, "FRONT": {"patternId": "7", "rotation": 0}, "BACK": {"patternId": "plus", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 270}, "RIGHT": {"patternId": "J", "rotation": 0}}, "bottom_faces": [{"patternId": "R", "rotation": 180, "x": 1, "y": 1}, {"patternId": "J", "rotation": 90, "x": 2, "y": 1}, {"patternId": "7", "rotation": 90, "x": 2, "y": 2}, {"patternId": "R", "rotation": 270, "x": 1, "y": 2}], "slot_sequence": ["RIGHT", "FRONT", "BOTTOM"], "required_slots": ["RIGHT", "FRONT", "BOTTOM"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "R", "rotation": 180}, "FRONT": {"patternId": "7", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "J", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "R", "rotation": 180}, "FRONT": {"patternId": "7", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "J", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C057\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=J, rotation=90, flipVertical=true\n- step 2: patternId=7, rotation=90, flipVertical=true\n- step 3: patternId=R, rotation=270, flipVertical=true\n- allowed patternId values for this task: J, 7, R, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C057"} +{"sample_id": "C058", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "N"], "observed_path_faces": [{"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C058_path_sequence.png"}, "metadata": {"level_id": 58, "name": "Reconstruct 058", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-058.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["J", "arrow_down", "8", "5", "G", "heart"], "start_x": 2, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "J", "rotation": 180}, "BOTTOM": {"patternId": "heart", "rotation": 180}, "FRONT": {"patternId": "arrow_down", "rotation": 270}, "BACK": {"patternId": "5", "rotation": 270}, "LEFT": {"patternId": "G", "rotation": 90}, "RIGHT": {"patternId": "8", "rotation": 90}}, "bottom_faces": [{"patternId": "heart", "rotation": 180, "x": 2, "y": 3}, {"patternId": "5", "rotation": 90, "x": 2, "y": 2}, {"patternId": "G", "rotation": 270, "x": 1, "y": 2}, {"patternId": "J", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["BACK", "LEFT", "TOP"], "required_slots": ["BACK", "LEFT", "TOP"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "J", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "5", "rotation": 90}, "LEFT": {"patternId": "G", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "J", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "5", "rotation": 90}, "LEFT": {"patternId": "G", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C058\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=5, rotation=90, flipVertical=true\n- step 2: patternId=G, rotation=270, flipVertical=true\n- step 3: patternId=J, rotation=270, flipVertical=true\n- allowed patternId values for this task: 5, G, J, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C058"} +{"sample_id": "C059", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "W"], "observed_path_faces": [{"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C059_path_sequence.png"}, "metadata": {"level_id": 59, "name": "Reconstruct 059", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-059.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["diamond", "G", "U", "9", "A", "heart"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 3, "true_solution_faces": {"TOP": {"patternId": "diamond", "rotation": 180}, "BOTTOM": {"patternId": "heart", "rotation": 0}, "FRONT": {"patternId": "G", "rotation": 270}, "BACK": {"patternId": "9", "rotation": 180}, "LEFT": {"patternId": "A", "rotation": 270}, "RIGHT": {"patternId": "U", "rotation": 180}}, "bottom_faces": [{"patternId": "heart", "rotation": 0, "x": 1, "y": 1}, {"patternId": "U", "rotation": 270, "x": 2, "y": 1}, {"patternId": "diamond", "rotation": 0, "x": 3, "y": 1}, {"patternId": "U", "rotation": 270, "x": 2, "y": 1}], "slot_sequence": ["RIGHT", "TOP", "RIGHT"], "required_slots": ["RIGHT", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "diamond", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "U", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "diamond", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "U", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C059\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=U, rotation=270, flipVertical=true\n- step 2: patternId=diamond, rotation=0, flipVertical=true\n- step 3: patternId=U, rotation=270, flipVertical=true\n- allowed patternId values for this task: U, diamond, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C059"} +{"sample_id": "C060", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N"], "observed_path_faces": [{"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C060_path_sequence.png"}, "metadata": {"level_id": 60, "name": "Reconstruct 060", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-060.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["F", "W", "3", "M", "star", "J"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "F", "rotation": 270}, "BOTTOM": {"patternId": "J", "rotation": 0}, "FRONT": {"patternId": "W", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 180}, "LEFT": {"patternId": "star", "rotation": 0}, "RIGHT": {"patternId": "3", "rotation": 180}}, "bottom_faces": [{"patternId": "J", "rotation": 0, "x": 1, "y": 2}, {"patternId": "3", "rotation": 270, "x": 2, "y": 2}, {"patternId": "M", "rotation": 270, "x": 2, "y": 1}], "slot_sequence": ["RIGHT", "BACK"], "required_slots": ["RIGHT", "BACK"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "3", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "3", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C060\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=3, rotation=270, flipVertical=true\n- step 2: patternId=M, rotation=270, flipVertical=true\n- allowed patternId values for this task: 3, M, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C060"} +{"sample_id": "C061", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W"], "observed_path_faces": [{"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C061_path_sequence.png"}, "metadata": {"level_id": 61, "name": "Reconstruct 061", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-061.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Z", "Q", "C", "arrow_up", "D", "heart"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 3, "true_solution_faces": {"TOP": {"patternId": "Z", "rotation": 0}, "BOTTOM": {"patternId": "heart", "rotation": 270}, "FRONT": {"patternId": "Q", "rotation": 0}, "BACK": {"patternId": "arrow_up", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 270}, "RIGHT": {"patternId": "C", "rotation": 180}}, "bottom_faces": [{"patternId": "heart", "rotation": 270, "x": 3, "y": 1}, {"patternId": "D", "rotation": 180, "x": 2, "y": 1}, {"patternId": "Z", "rotation": 180, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "TOP"], "required_slots": ["LEFT", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "Z", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "Z", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C061\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=D, rotation=180, flipVertical=true\n- step 2: patternId=Z, rotation=180, flipVertical=true\n- allowed patternId values for this task: D, Z, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C061"} +{"sample_id": "C062", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E"], "observed_path_faces": [{"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C062_path_sequence.png"}, "metadata": {"level_id": 62, "name": "Reconstruct 062", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-062.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["L", "F", "C", "7", "arrow_left", "triangle"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 3, "true_solution_faces": {"TOP": {"patternId": "L", "rotation": 90}, "BOTTOM": {"patternId": "triangle", "rotation": 180}, "FRONT": {"patternId": "F", "rotation": 0}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "arrow_left", "rotation": 180}, "RIGHT": {"patternId": "C", "rotation": 270}}, "bottom_faces": [{"patternId": "triangle", "rotation": 180, "x": 1, "y": 1}, {"patternId": "C", "rotation": 0, "x": 2, "y": 1}, {"patternId": "L", "rotation": 270, "x": 3, "y": 1}], "slot_sequence": ["RIGHT", "TOP"], "required_slots": ["RIGHT", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "L", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "C", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "L", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "C", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C062\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=C, rotation=0, flipVertical=true\n- step 2: patternId=L, rotation=270, flipVertical=true\n- allowed patternId values for this task: C, L, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C062"} +{"sample_id": "C063", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N"], "observed_path_faces": [{"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C063_path_sequence.png"}, "metadata": {"level_id": 63, "name": "Reconstruct 063", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-063.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["H", "O", "K", "triangle", "circle", "T"], "start_x": 1, "start_y": 3, "grid_width": 3, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "H", "rotation": 0}, "BOTTOM": {"patternId": "T", "rotation": 270}, "FRONT": {"patternId": "O", "rotation": 180}, "BACK": {"patternId": "triangle", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 270}, "RIGHT": {"patternId": "K", "rotation": 90}}, "bottom_faces": [{"patternId": "T", "rotation": 270, "x": 1, "y": 3}, {"patternId": "triangle", "rotation": 180, "x": 1, "y": 2}, {"patternId": "H", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["BACK", "TOP"], "required_slots": ["BACK", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "H", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "triangle", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "H", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "triangle", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C063\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=triangle, rotation=180, flipVertical=true\n- step 2: patternId=H, rotation=0, flipVertical=true\n- allowed patternId values for this task: triangle, H, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C063"} +{"sample_id": "C064", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "S"], "observed_path_faces": [{"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C064_path_sequence.png"}, "metadata": {"level_id": 64, "name": "Reconstruct 064", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-064.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["O", "A", "arrow_up", "S", "W", "R"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "R", "rotation": 180}, "FRONT": {"patternId": "A", "rotation": 270}, "BACK": {"patternId": "S", "rotation": 90}, "LEFT": {"patternId": "W", "rotation": 270}, "RIGHT": {"patternId": "arrow_up", "rotation": 90}}, "bottom_faces": [{"patternId": "R", "rotation": 180, "x": 2, "y": 1}, {"patternId": "A", "rotation": 270, "x": 2, "y": 2}, {"patternId": "W", "rotation": 270, "x": 1, "y": 2}, {"patternId": "O", "rotation": 180, "x": 1, "y": 3}], "slot_sequence": ["FRONT", "LEFT", "TOP"], "required_slots": ["FRONT", "LEFT", "TOP"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "A", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "A", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C064\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=A, rotation=270, flipVertical=true\n- step 2: patternId=W, rotation=270, flipVertical=true\n- step 3: patternId=O, rotation=180, flipVertical=true\n- allowed patternId values for this task: A, W, O, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C064"} +{"sample_id": "C065", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E"], "observed_path_faces": [{"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C065_path_sequence.png"}, "metadata": {"level_id": 65, "name": "Reconstruct 065", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-065.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["H", "S", "Z", "4", "L", "C"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 3, "true_solution_faces": {"TOP": {"patternId": "H", "rotation": 90}, "BOTTOM": {"patternId": "C", "rotation": 90}, "FRONT": {"patternId": "S", "rotation": 180}, "BACK": {"patternId": "4", "rotation": 180}, "LEFT": {"patternId": "L", "rotation": 90}, "RIGHT": {"patternId": "Z", "rotation": 270}}, "bottom_faces": [{"patternId": "C", "rotation": 90, "x": 1, "y": 1}, {"patternId": "Z", "rotation": 0, "x": 2, "y": 1}, {"patternId": "H", "rotation": 270, "x": 3, "y": 1}], "slot_sequence": ["RIGHT", "TOP"], "required_slots": ["RIGHT", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "H", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "H", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C065\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Z, rotation=0, flipVertical=true\n- step 2: patternId=H, rotation=270, flipVertical=true\n- allowed patternId values for this task: Z, H, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C065"} +{"sample_id": "C066", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "N"], "observed_path_faces": [{"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C066_path_sequence.png"}, "metadata": {"level_id": 66, "name": "Reconstruct 066", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-066.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Q", "A", "R", "B", "V", "triangle"], "start_x": 1, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "Q", "rotation": 0}, "BOTTOM": {"patternId": "triangle", "rotation": 180}, "FRONT": {"patternId": "A", "rotation": 90}, "BACK": {"patternId": "B", "rotation": 90}, "LEFT": {"patternId": "V", "rotation": 180}, "RIGHT": {"patternId": "R", "rotation": 0}}, "bottom_faces": [{"patternId": "triangle", "rotation": 180, "x": 1, "y": 3}, {"patternId": "R", "rotation": 90, "x": 2, "y": 3}, {"patternId": "B", "rotation": 180, "x": 2, "y": 2}, {"patternId": "V", "rotation": 270, "x": 2, "y": 1}], "slot_sequence": ["RIGHT", "BACK", "LEFT"], "required_slots": ["RIGHT", "BACK", "LEFT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 270}, "LEFT": {"patternId": "V", "rotation": 270}, "RIGHT": {"patternId": "R", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 270}, "LEFT": {"patternId": "V", "rotation": 270}, "RIGHT": {"patternId": "R", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C066\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=R, rotation=90, flipVertical=true\n- step 2: patternId=B, rotation=180, flipVertical=true\n- step 3: patternId=V, rotation=270, flipVertical=true\n- allowed patternId values for this task: R, B, V, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C066"} +{"sample_id": "C067", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "N"], "observed_path_faces": [{"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C067_path_sequence.png"}, "metadata": {"level_id": 67, "name": "Reconstruct 067", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-067.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["9", "1", "B", "Y", "1", "F"], "start_x": 2, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "9", "rotation": 180}, "BOTTOM": {"patternId": "F", "rotation": 180}, "FRONT": {"patternId": "1", "rotation": 0}, "BACK": {"patternId": "Y", "rotation": 270}, "LEFT": {"patternId": "1", "rotation": 0}, "RIGHT": {"patternId": "B", "rotation": 270}}, "bottom_faces": [{"patternId": "F", "rotation": 180, "x": 2, "y": 3}, {"patternId": "Y", "rotation": 90, "x": 2, "y": 2}, {"patternId": "1", "rotation": 180, "x": 1, "y": 2}, {"patternId": "9", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["BACK", "LEFT", "TOP"], "required_slots": ["BACK", "LEFT", "TOP"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "9", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "Y", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "9", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "Y", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C067\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Y, rotation=90, flipVertical=true\n- step 2: patternId=1, rotation=180, flipVertical=true\n- step 3: patternId=9, rotation=270, flipVertical=true\n- allowed patternId values for this task: Y, 1, 9, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C067"} +{"sample_id": "C068", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S"], "observed_path_faces": [{"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C068_path_sequence.png"}, "metadata": {"level_id": 68, "name": "Reconstruct 068", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-068.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["7", "diamond", "D", "Q", "arrow_right", "heart"], "start_x": 1, "start_y": 1, "grid_width": 3, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "7", "rotation": 270}, "BOTTOM": {"patternId": "heart", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 270}, "BACK": {"patternId": "Q", "rotation": 0}, "LEFT": {"patternId": "arrow_right", "rotation": 270}, "RIGHT": {"patternId": "D", "rotation": 180}}, "bottom_faces": [{"patternId": "heart", "rotation": 0, "x": 1, "y": 1}, {"patternId": "diamond", "rotation": 270, "x": 1, "y": 2}, {"patternId": "7", "rotation": 270, "x": 1, "y": 3}], "slot_sequence": ["FRONT", "TOP"], "required_slots": ["FRONT", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "7", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "7", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C068\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=diamond, rotation=270, flipVertical=true\n- step 2: patternId=7, rotation=270, flipVertical=true\n- allowed patternId values for this task: diamond, 7, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C068"} +{"sample_id": "C069", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "S"], "observed_path_faces": [{"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C069_path_sequence.png"}, "metadata": {"level_id": 69, "name": "Reconstruct 069", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-069.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["K", "H", "V", "O", "square", "Q"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "K", "rotation": 90}, "BOTTOM": {"patternId": "Q", "rotation": 180}, "FRONT": {"patternId": "H", "rotation": 270}, "BACK": {"patternId": "O", "rotation": 270}, "LEFT": {"patternId": "square", "rotation": 90}, "RIGHT": {"patternId": "V", "rotation": 90}}, "bottom_faces": [{"patternId": "Q", "rotation": 180, "x": 1, "y": 1}, {"patternId": "V", "rotation": 180, "x": 2, "y": 1}, {"patternId": "H", "rotation": 0, "x": 2, "y": 2}, {"patternId": "square", "rotation": 180, "x": 2, "y": 3}], "slot_sequence": ["RIGHT", "FRONT", "LEFT"], "required_slots": ["RIGHT", "FRONT", "LEFT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "square", "rotation": 180}, "RIGHT": {"patternId": "V", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "square", "rotation": 180}, "RIGHT": {"patternId": "V", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C069\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=V, rotation=180, flipVertical=true\n- step 2: patternId=H, rotation=0, flipVertical=true\n- step 3: patternId=square, rotation=180, flipVertical=true\n- allowed patternId values for this task: V, H, square, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C069"} +{"sample_id": "C070", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "W"], "observed_path_faces": [{"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C070_path_sequence.png"}, "metadata": {"level_id": 70, "name": "Reconstruct 070", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-070.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["N", "circle", "heart", "K", "6", "C"], "start_x": 4, "start_y": 1, "grid_width": 6, "grid_height": 3, "true_solution_faces": {"TOP": {"patternId": "N", "rotation": 0}, "BOTTOM": {"patternId": "C", "rotation": 90}, "FRONT": {"patternId": "circle", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "6", "rotation": 270}, "RIGHT": {"patternId": "heart", "rotation": 180}}, "bottom_faces": [{"patternId": "C", "rotation": 90, "x": 4, "y": 1}, {"patternId": "6", "rotation": 180, "x": 3, "y": 1}, {"patternId": "N", "rotation": 180, "x": 2, "y": 1}, {"patternId": "heart", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "TOP", "RIGHT"], "required_slots": ["LEFT", "TOP", "RIGHT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "N", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "6", "rotation": 0}, "RIGHT": {"patternId": "heart", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "N", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "6", "rotation": 0}, "RIGHT": {"patternId": "heart", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C070\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=6, rotation=180, flipVertical=true\n- step 2: patternId=N, rotation=180, flipVertical=true\n- step 3: patternId=heart, rotation=270, flipVertical=true\n- allowed patternId values for this task: 6, N, heart, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C070"} +{"sample_id": "C071", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S"], "observed_path_faces": [{"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C071_path_sequence.png"}, "metadata": {"level_id": 71, "name": "Reconstruct 071", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-071.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["circle", "H", "arrow_left", "Z", "4", "9"], "start_x": 1, "start_y": 1, "grid_width": 3, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "circle", "rotation": 90}, "BOTTOM": {"patternId": "9", "rotation": 270}, "FRONT": {"patternId": "H", "rotation": 0}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "4", "rotation": 180}, "RIGHT": {"patternId": "arrow_left", "rotation": 180}}, "bottom_faces": [{"patternId": "9", "rotation": 270, "x": 1, "y": 1}, {"patternId": "H", "rotation": 0, "x": 1, "y": 2}, {"patternId": "circle", "rotation": 90, "x": 1, "y": 3}], "slot_sequence": ["FRONT", "TOP"], "required_slots": ["FRONT", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "circle", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C071\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=H, rotation=0, flipVertical=true\n- step 2: patternId=circle, rotation=90, flipVertical=true\n- allowed patternId values for this task: H, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C071"} +{"sample_id": "C072", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "E"], "observed_path_faces": [{"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C072_path_sequence.png"}, "metadata": {"level_id": 72, "name": "Reconstruct 072", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-072.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["6", "D", "arrow_left", "R", "plus", "J"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "6", "rotation": 90}, "BOTTOM": {"patternId": "J", "rotation": 90}, "FRONT": {"patternId": "D", "rotation": 270}, "BACK": {"patternId": "R", "rotation": 90}, "LEFT": {"patternId": "plus", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 270}}, "bottom_faces": [{"patternId": "J", "rotation": 90, "x": 1, "y": 1}, {"patternId": "arrow_left", "rotation": 0, "x": 2, "y": 1}, {"patternId": "D", "rotation": 0, "x": 2, "y": 2}, {"patternId": "6", "rotation": 180, "x": 3, "y": 2}], "slot_sequence": ["RIGHT", "FRONT", "TOP"], "required_slots": ["RIGHT", "FRONT", "TOP"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "6", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C072\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_left, rotation=0, flipVertical=true\n- step 2: patternId=D, rotation=0, flipVertical=true\n- step 3: patternId=6, rotation=180, flipVertical=true\n- allowed patternId values for this task: arrow_left, D, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C072"} +{"sample_id": "C073", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W"], "observed_path_faces": [{"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C073_path_sequence.png"}, "metadata": {"level_id": 73, "name": "Reconstruct 073", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-073.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["M", "X", "smile", "W", "5", "L"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "M", "rotation": 0}, "BOTTOM": {"patternId": "L", "rotation": 180}, "FRONT": {"patternId": "X", "rotation": 90}, "BACK": {"patternId": "W", "rotation": 0}, "LEFT": {"patternId": "5", "rotation": 0}, "RIGHT": {"patternId": "smile", "rotation": 90}}, "bottom_faces": [{"patternId": "L", "rotation": 180, "x": 2, "y": 1}, {"patternId": "X", "rotation": 90, "x": 2, "y": 2}, {"patternId": "5", "rotation": 0, "x": 1, "y": 2}], "slot_sequence": ["FRONT", "LEFT"], "required_slots": ["FRONT", "LEFT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "X", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "5", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "X", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "5", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C073\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=X, rotation=90, flipVertical=true\n- step 2: patternId=5, rotation=0, flipVertical=true\n- allowed patternId values for this task: X, 5, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C073"} +{"sample_id": "C074", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N"], "observed_path_faces": [{"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C074_path_sequence.png"}, "metadata": {"level_id": 74, "name": "Reconstruct 074", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-074.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["R", "O", "O", "C", "S", "arrow_left"], "start_x": 2, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "R", "rotation": 180}, "BOTTOM": {"patternId": "arrow_left", "rotation": 90}, "FRONT": {"patternId": "O", "rotation": 180}, "BACK": {"patternId": "C", "rotation": 180}, "LEFT": {"patternId": "S", "rotation": 180}, "RIGHT": {"patternId": "O", "rotation": 270}}, "bottom_faces": [{"patternId": "arrow_left", "rotation": 90, "x": 2, "y": 2}, {"patternId": "S", "rotation": 90, "x": 1, "y": 2}, {"patternId": "C", "rotation": 90, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "BACK"], "required_slots": ["LEFT", "BACK"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "C", "rotation": 0}, "LEFT": {"patternId": "S", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "C", "rotation": 0}, "LEFT": {"patternId": "S", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C074\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=S, rotation=90, flipVertical=true\n- step 2: patternId=C, rotation=90, flipVertical=true\n- allowed patternId values for this task: S, C, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C074"} +{"sample_id": "C075", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "E"], "observed_path_faces": [{"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C075_path_sequence.png"}, "metadata": {"level_id": 75, "name": "Reconstruct 075", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-075.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["6", "F", "6", "3", "arrow_down", "C"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "6", "rotation": 0}, "BOTTOM": {"patternId": "C", "rotation": 180}, "FRONT": {"patternId": "F", "rotation": 180}, "BACK": {"patternId": "3", "rotation": 90}, "LEFT": {"patternId": "arrow_down", "rotation": 270}, "RIGHT": {"patternId": "6", "rotation": 270}}, "bottom_faces": [{"patternId": "C", "rotation": 180, "x": 1, "y": 1}, {"patternId": "6", "rotation": 0, "x": 2, "y": 1}, {"patternId": "F", "rotation": 270, "x": 2, "y": 2}, {"patternId": "6", "rotation": 90, "x": 3, "y": 2}], "slot_sequence": ["RIGHT", "FRONT", "TOP"], "required_slots": ["RIGHT", "FRONT", "TOP"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "6", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "F", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "F", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C075\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=6, rotation=0, flipVertical=true\n- step 2: patternId=F, rotation=270, flipVertical=true\n- step 3: patternId=6, rotation=90, flipVertical=true\n- allowed patternId values for this task: 6, F, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C075"} +{"sample_id": "C076", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N"], "observed_path_faces": [{"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C076_path_sequence.png"}, "metadata": {"level_id": 76, "name": "Reconstruct 076", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-076.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["X", "square", "star", "F", "6", "K"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "X", "rotation": 270}, "BOTTOM": {"patternId": "K", "rotation": 180}, "FRONT": {"patternId": "square", "rotation": 270}, "BACK": {"patternId": "F", "rotation": 90}, "LEFT": {"patternId": "6", "rotation": 90}, "RIGHT": {"patternId": "star", "rotation": 270}}, "bottom_faces": [{"patternId": "K", "rotation": 180, "x": 1, "y": 2}, {"patternId": "star", "rotation": 0, "x": 2, "y": 2}, {"patternId": "F", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["RIGHT", "BACK"], "required_slots": ["RIGHT", "BACK"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "F", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "star", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "F", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "star", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C076\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=star, rotation=0, flipVertical=true\n- step 2: patternId=F, rotation=180, flipVertical=true\n- allowed patternId values for this task: star, F, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C076"} +{"sample_id": "C077", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "S"], "observed_path_faces": [{"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C077_path_sequence.png"}, "metadata": {"level_id": 77, "name": "Reconstruct 077", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-077.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["7", "J", "Y", "M", "heart", "E"], "start_x": 1, "start_y": 1, "grid_width": 3, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "7", "rotation": 180}, "BOTTOM": {"patternId": "E", "rotation": 90}, "FRONT": {"patternId": "J", "rotation": 270}, "BACK": {"patternId": "M", "rotation": 270}, "LEFT": {"patternId": "heart", "rotation": 180}, "RIGHT": {"patternId": "Y", "rotation": 180}}, "bottom_faces": [{"patternId": "E", "rotation": 90, "x": 1, "y": 1}, {"patternId": "J", "rotation": 270, "x": 1, "y": 2}, {"patternId": "7", "rotation": 180, "x": 1, "y": 3}, {"patternId": "M", "rotation": 90, "x": 1, "y": 4}], "slot_sequence": ["FRONT", "TOP", "BACK"], "required_slots": ["FRONT", "TOP", "BACK"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "7", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 270}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "7", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 270}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C077\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=J, rotation=270, flipVertical=true\n- step 2: patternId=7, rotation=180, flipVertical=true\n- step 3: patternId=M, rotation=90, flipVertical=true\n- allowed patternId values for this task: J, 7, M, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C077"} +{"sample_id": "C078", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W"], "observed_path_faces": [{"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C078_path_sequence.png"}, "metadata": {"level_id": 78, "name": "Reconstruct 078", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-078.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["M", "Q", "A", "6", "E", "arrow_left"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 3, "true_solution_faces": {"TOP": {"patternId": "M", "rotation": 270}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "Q", "rotation": 180}, "BACK": {"patternId": "6", "rotation": 270}, "LEFT": {"patternId": "E", "rotation": 180}, "RIGHT": {"patternId": "A", "rotation": 270}}, "bottom_faces": [{"patternId": "arrow_left", "rotation": 0, "x": 3, "y": 1}, {"patternId": "E", "rotation": 90, "x": 2, "y": 1}, {"patternId": "M", "rotation": 90, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "TOP"], "required_slots": ["LEFT", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "M", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "E", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "E", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C078\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=E, rotation=90, flipVertical=true\n- step 2: patternId=M, rotation=90, flipVertical=true\n- allowed patternId values for this task: E, M, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C078"} +{"sample_id": "C079", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E"], "observed_path_faces": [{"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C079_path_sequence.png"}, "metadata": {"level_id": 79, "name": "Reconstruct 079", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-079.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Q", "triangle", "star", "arrow_left", "S", "N"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 3, "true_solution_faces": {"TOP": {"patternId": "Q", "rotation": 270}, "BOTTOM": {"patternId": "N", "rotation": 90}, "FRONT": {"patternId": "triangle", "rotation": 180}, "BACK": {"patternId": "arrow_left", "rotation": 90}, "LEFT": {"patternId": "S", "rotation": 0}, "RIGHT": {"patternId": "star", "rotation": 90}}, "bottom_faces": [{"patternId": "N", "rotation": 90, "x": 1, "y": 1}, {"patternId": "star", "rotation": 180, "x": 2, "y": 1}, {"patternId": "Q", "rotation": 90, "x": 3, "y": 1}], "slot_sequence": ["RIGHT", "TOP"], "required_slots": ["RIGHT", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "Q", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "star", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "Q", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "star", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C079\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=star, rotation=180, flipVertical=true\n- step 2: patternId=Q, rotation=90, flipVertical=true\n- allowed patternId values for this task: star, Q, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C079"} +{"sample_id": "C080", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S"], "observed_path_faces": [{"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C080_path_sequence.png"}, "metadata": {"level_id": 80, "name": "Reconstruct 080", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-080.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_left", "plus", "6", "circle", "square", "7"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "arrow_left", "rotation": 270}, "BOTTOM": {"patternId": "7", "rotation": 270}, "FRONT": {"patternId": "plus", "rotation": 270}, "BACK": {"patternId": "circle", "rotation": 180}, "LEFT": {"patternId": "square", "rotation": 270}, "RIGHT": {"patternId": "6", "rotation": 270}}, "bottom_faces": [{"patternId": "7", "rotation": 270, "x": 1, "y": 1}, {"patternId": "6", "rotation": 0, "x": 2, "y": 1}, {"patternId": "plus", "rotation": 0, "x": 2, "y": 2}], "slot_sequence": ["RIGHT", "FRONT"], "required_slots": ["RIGHT", "FRONT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "plus", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "plus", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C080\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=6, rotation=0, flipVertical=true\n- step 2: patternId=plus, rotation=0, flipVertical=true\n- allowed patternId values for this task: 6, plus, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C080"} +{"sample_id": "C081", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "S"], "observed_path_faces": [{"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C081_path_sequence.png"}, "metadata": {"level_id": 81, "name": "Reconstruct 081", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-081.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["G", "E", "P", "plus", "C", "1"], "start_x": 2, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "G", "rotation": 270}, "BOTTOM": {"patternId": "1", "rotation": 90}, "FRONT": {"patternId": "E", "rotation": 90}, "BACK": {"patternId": "plus", "rotation": 90}, "LEFT": {"patternId": "C", "rotation": 180}, "RIGHT": {"patternId": "P", "rotation": 270}}, "bottom_faces": [{"patternId": "1", "rotation": 90, "x": 2, "y": 2}, {"patternId": "C", "rotation": 90, "x": 1, "y": 2}, {"patternId": "plus", "rotation": 0, "x": 1, "y": 1}, {"patternId": "C", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["LEFT", "BACK", "LEFT"], "required_slots": ["LEFT", "BACK"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "plus", "rotation": 270}, "LEFT": {"patternId": "C", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "plus", "rotation": 270}, "LEFT": {"patternId": "C", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C081\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=C, rotation=90, flipVertical=true\n- step 2: patternId=plus, rotation=0, flipVertical=true\n- step 3: patternId=C, rotation=90, flipVertical=true\n- allowed patternId values for this task: C, plus, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C081"} +{"sample_id": "C082", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "N"], "observed_path_faces": [{"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C082_path_sequence.png"}, "metadata": {"level_id": 82, "name": "Reconstruct 082", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-082.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["star", "8", "Q", "C", "Y", "6"], "start_x": 1, "start_y": 1, "grid_width": 3, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "star", "rotation": 180}, "BOTTOM": {"patternId": "6", "rotation": 0}, "FRONT": {"patternId": "8", "rotation": 90}, "BACK": {"patternId": "C", "rotation": 270}, "LEFT": {"patternId": "Y", "rotation": 0}, "RIGHT": {"patternId": "Q", "rotation": 270}}, "bottom_faces": [{"patternId": "6", "rotation": 0, "x": 1, "y": 1}, {"patternId": "8", "rotation": 90, "x": 1, "y": 2}, {"patternId": "6", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["FRONT", "BOTTOM"], "required_slots": ["FRONT", "BOTTOM"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 0}, "FRONT": {"patternId": "8", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 0}, "FRONT": {"patternId": "8", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C082\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=8, rotation=90, flipVertical=true\n- step 2: patternId=6, rotation=0, flipVertical=true\n- allowed patternId values for this task: 8, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C082"} +{"sample_id": "C083", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E"], "observed_path_faces": [{"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C083_path_sequence.png"}, "metadata": {"level_id": 83, "name": "Reconstruct 083", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-083.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["L", "8", "1", "P", "O", "F"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "L", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 0}, "FRONT": {"patternId": "8", "rotation": 270}, "BACK": {"patternId": "P", "rotation": 90}, "LEFT": {"patternId": "O", "rotation": 270}, "RIGHT": {"patternId": "1", "rotation": 180}}, "bottom_faces": [{"patternId": "F", "rotation": 0, "x": 1, "y": 1}, {"patternId": "8", "rotation": 270, "x": 1, "y": 2}, {"patternId": "1", "rotation": 180, "x": 2, "y": 2}], "slot_sequence": ["FRONT", "RIGHT"], "required_slots": ["FRONT", "RIGHT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "8", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "8", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C083\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=8, rotation=270, flipVertical=true\n- step 2: patternId=1, rotation=180, flipVertical=true\n- allowed patternId values for this task: 8, 1, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C083"} +{"sample_id": "C084", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "S"], "observed_path_faces": [{"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C084_path_sequence.png"}, "metadata": {"level_id": 84, "name": "Reconstruct 084", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-084.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["9", "heart", "V", "2", "3", "Y"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "9", "rotation": 0}, "BOTTOM": {"patternId": "Y", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 180}, "BACK": {"patternId": "2", "rotation": 90}, "LEFT": {"patternId": "3", "rotation": 90}, "RIGHT": {"patternId": "V", "rotation": 90}}, "bottom_faces": [{"patternId": "Y", "rotation": 0, "x": 1, "y": 1}, {"patternId": "V", "rotation": 180, "x": 2, "y": 1}, {"patternId": "heart", "rotation": 270, "x": 2, "y": 2}, {"patternId": "3", "rotation": 180, "x": 2, "y": 3}], "slot_sequence": ["RIGHT", "FRONT", "LEFT"], "required_slots": ["RIGHT", "FRONT", "LEFT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 180}, "RIGHT": {"patternId": "V", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 180}, "RIGHT": {"patternId": "V", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C084\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=V, rotation=180, flipVertical=true\n- step 2: patternId=heart, rotation=270, flipVertical=true\n- step 3: patternId=3, rotation=180, flipVertical=true\n- allowed patternId values for this task: V, heart, 3, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C084"} +{"sample_id": "C085", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W"], "observed_path_faces": [{"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C085_path_sequence.png"}, "metadata": {"level_id": 85, "name": "Reconstruct 085", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-085.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["C", "7", "2", "heart", "square", "arrow_up"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "C", "rotation": 180}, "BOTTOM": {"patternId": "arrow_up", "rotation": 180}, "FRONT": {"patternId": "7", "rotation": 270}, "BACK": {"patternId": "heart", "rotation": 90}, "LEFT": {"patternId": "square", "rotation": 90}, "RIGHT": {"patternId": "2", "rotation": 270}}, "bottom_faces": [{"patternId": "arrow_up", "rotation": 180, "x": 2, "y": 1}, {"patternId": "7", "rotation": 270, "x": 2, "y": 2}, {"patternId": "square", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["FRONT", "LEFT"], "required_slots": ["FRONT", "LEFT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "square", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "square", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C085\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=7, rotation=270, flipVertical=true\n- step 2: patternId=square, rotation=90, flipVertical=true\n- allowed patternId values for this task: 7, square, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C085"} +{"sample_id": "C086", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W"], "observed_path_faces": [{"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C086_path_sequence.png"}, "metadata": {"level_id": 86, "name": "Reconstruct 086", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-086.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["2", "7", "circle", "K", "U", "I"], "start_x": 2, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "2", "rotation": 0}, "BOTTOM": {"patternId": "I", "rotation": 270}, "FRONT": {"patternId": "7", "rotation": 180}, "BACK": {"patternId": "K", "rotation": 90}, "LEFT": {"patternId": "U", "rotation": 270}, "RIGHT": {"patternId": "circle", "rotation": 0}}, "bottom_faces": [{"patternId": "I", "rotation": 270, "x": 2, "y": 2}, {"patternId": "K", "rotation": 270, "x": 2, "y": 1}, {"patternId": "U", "rotation": 90, "x": 1, "y": 1}], "slot_sequence": ["BACK", "LEFT"], "required_slots": ["BACK", "LEFT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "U", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "U", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C086\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=K, rotation=270, flipVertical=true\n- step 2: patternId=U, rotation=90, flipVertical=true\n- allowed patternId values for this task: K, U, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C086"} +{"sample_id": "C087", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E"], "observed_path_faces": [{"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C087_path_sequence.png"}, "metadata": {"level_id": 87, "name": "Reconstruct 087", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-087.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["E", "7", "circle", "I", "N", "H"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "E", "rotation": 270}, "BOTTOM": {"patternId": "H", "rotation": 180}, "FRONT": {"patternId": "7", "rotation": 90}, "BACK": {"patternId": "I", "rotation": 180}, "LEFT": {"patternId": "N", "rotation": 90}, "RIGHT": {"patternId": "circle", "rotation": 90}}, "bottom_faces": [{"patternId": "H", "rotation": 180, "x": 1, "y": 1}, {"patternId": "7", "rotation": 90, "x": 1, "y": 2}, {"patternId": "circle", "rotation": 90, "x": 2, "y": 2}], "slot_sequence": ["FRONT", "RIGHT"], "required_slots": ["FRONT", "RIGHT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "circle", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "circle", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C087\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=7, rotation=90, flipVertical=true\n- step 2: patternId=circle, rotation=90, flipVertical=true\n- allowed patternId values for this task: 7, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C087"} +{"sample_id": "C088", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "N"], "observed_path_faces": [{"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C088_path_sequence.png"}, "metadata": {"level_id": 88, "name": "Reconstruct 088", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-088.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["1", "star", "V", "G", "1", "plus"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "1", "rotation": 90}, "BOTTOM": {"patternId": "plus", "rotation": 180}, "FRONT": {"patternId": "star", "rotation": 270}, "BACK": {"patternId": "G", "rotation": 0}, "LEFT": {"patternId": "1", "rotation": 0}, "RIGHT": {"patternId": "V", "rotation": 0}}, "bottom_faces": [{"patternId": "plus", "rotation": 180, "x": 2, "y": 1}, {"patternId": "star", "rotation": 270, "x": 2, "y": 2}, {"patternId": "1", "rotation": 0, "x": 1, "y": 2}, {"patternId": "plus", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["FRONT", "LEFT", "BOTTOM"], "required_slots": ["FRONT", "LEFT", "BOTTOM"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "plus", "rotation": 180}, "FRONT": {"patternId": "star", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "1", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "plus", "rotation": 180}, "FRONT": {"patternId": "star", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "1", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C088\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=star, rotation=270, flipVertical=true\n- step 2: patternId=1, rotation=0, flipVertical=true\n- step 3: patternId=plus, rotation=270, flipVertical=true\n- allowed patternId values for this task: star, 1, plus, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C088"} +{"sample_id": "C089", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E"], "observed_path_faces": [{"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C089_path_sequence.png"}, "metadata": {"level_id": 89, "name": "Reconstruct 089", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-089.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["W", "7", "Y", "4", "2", "heart"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "W", "rotation": 0}, "BOTTOM": {"patternId": "heart", "rotation": 180}, "FRONT": {"patternId": "7", "rotation": 270}, "BACK": {"patternId": "4", "rotation": 180}, "LEFT": {"patternId": "2", "rotation": 270}, "RIGHT": {"patternId": "Y", "rotation": 0}}, "bottom_faces": [{"patternId": "heart", "rotation": 180, "x": 1, "y": 2}, {"patternId": "4", "rotation": 0, "x": 1, "y": 1}, {"patternId": "Y", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["BACK", "RIGHT"], "required_slots": ["BACK", "RIGHT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "4", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Y", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "4", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Y", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C089\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=4, rotation=0, flipVertical=true\n- step 2: patternId=Y, rotation=180, flipVertical=true\n- allowed patternId values for this task: 4, Y, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C089"} +{"sample_id": "C090", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "N"], "observed_path_faces": [{"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C090_path_sequence.png"}, "metadata": {"level_id": 90, "name": "Reconstruct 090", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-090.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["S", "A", "I", "circle", "arrow_right", "O"], "start_x": 1, "start_y": 2, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "S", "rotation": 270}, "BOTTOM": {"patternId": "O", "rotation": 90}, "FRONT": {"patternId": "A", "rotation": 180}, "BACK": {"patternId": "circle", "rotation": 90}, "LEFT": {"patternId": "arrow_right", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 0}}, "bottom_faces": [{"patternId": "O", "rotation": 90, "x": 1, "y": 2}, {"patternId": "I", "rotation": 90, "x": 2, "y": 2}, {"patternId": "S", "rotation": 90, "x": 3, "y": 2}, {"patternId": "circle", "rotation": 90, "x": 3, "y": 1}], "slot_sequence": ["RIGHT", "TOP", "BACK"], "required_slots": ["RIGHT", "TOP", "BACK"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "S", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C090\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=I, rotation=90, flipVertical=true\n- step 2: patternId=S, rotation=90, flipVertical=true\n- step 3: patternId=circle, rotation=90, flipVertical=true\n- allowed patternId values for this task: I, S, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C090"} +{"sample_id": "C091", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E"], "observed_path_faces": [{"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C091_path_sequence.png"}, "metadata": {"level_id": 91, "name": "Reconstruct 091", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-091.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["smile", "smile", "P", "arrow_up", "arrow_down", "D"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 3, "true_solution_faces": {"TOP": {"patternId": "smile", "rotation": 270}, "BOTTOM": {"patternId": "D", "rotation": 180}, "FRONT": {"patternId": "smile", "rotation": 270}, "BACK": {"patternId": "arrow_up", "rotation": 0}, "LEFT": {"patternId": "arrow_down", "rotation": 270}, "RIGHT": {"patternId": "P", "rotation": 270}}, "bottom_faces": [{"patternId": "D", "rotation": 180, "x": 1, "y": 1}, {"patternId": "P", "rotation": 0, "x": 2, "y": 1}, {"patternId": "smile", "rotation": 90, "x": 3, "y": 1}], "slot_sequence": ["RIGHT", "TOP"], "required_slots": ["RIGHT", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "smile", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "P", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "P", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C091\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=P, rotation=0, flipVertical=true\n- step 2: patternId=smile, rotation=90, flipVertical=true\n- allowed patternId values for this task: P, smile, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C091"} +{"sample_id": "C092", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S"], "observed_path_faces": [{"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C092_path_sequence.png"}, "metadata": {"level_id": 92, "name": "Reconstruct 092", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-092.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["plus", "H", "D", "6", "W", "7"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "plus", "rotation": 0}, "BOTTOM": {"patternId": "7", "rotation": 90}, "FRONT": {"patternId": "H", "rotation": 270}, "BACK": {"patternId": "6", "rotation": 270}, "LEFT": {"patternId": "W", "rotation": 180}, "RIGHT": {"patternId": "D", "rotation": 180}}, "bottom_faces": [{"patternId": "7", "rotation": 90, "x": 2, "y": 1}, {"patternId": "W", "rotation": 90, "x": 1, "y": 1}, {"patternId": "H", "rotation": 180, "x": 1, "y": 2}], "slot_sequence": ["LEFT", "FRONT"], "required_slots": ["LEFT", "FRONT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C092\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=W, rotation=90, flipVertical=true\n- step 2: patternId=H, rotation=180, flipVertical=true\n- allowed patternId values for this task: W, H, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C092"} +{"sample_id": "C093", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N"], "observed_path_faces": [{"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C093_path_sequence.png"}, "metadata": {"level_id": 93, "name": "Reconstruct 093", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-093.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["6", "7", "5", "heart", "3", "square"], "start_x": 1, "start_y": 3, "grid_width": 3, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "6", "rotation": 90}, "BOTTOM": {"patternId": "square", "rotation": 270}, "FRONT": {"patternId": "7", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 90}, "RIGHT": {"patternId": "5", "rotation": 0}}, "bottom_faces": [{"patternId": "square", "rotation": 270, "x": 1, "y": 3}, {"patternId": "heart", "rotation": 180, "x": 1, "y": 2}, {"patternId": "6", "rotation": 90, "x": 1, "y": 1}], "slot_sequence": ["BACK", "TOP"], "required_slots": ["BACK", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "6", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C093\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=heart, rotation=180, flipVertical=true\n- step 2: patternId=6, rotation=90, flipVertical=true\n- allowed patternId values for this task: heart, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C093"} +{"sample_id": "C094", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "E"], "observed_path_faces": [{"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C094_path_sequence.png"}, "metadata": {"level_id": 94, "name": "Reconstruct 094", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-094.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["plus", "heart", "M", "smile", "3", "Z"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 3, "true_solution_faces": {"TOP": {"patternId": "plus", "rotation": 180}, "BOTTOM": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "heart", "rotation": 0}, "BACK": {"patternId": "smile", "rotation": 270}, "LEFT": {"patternId": "3", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 90}}, "bottom_faces": [{"patternId": "Z", "rotation": 270, "x": 2, "y": 1}, {"patternId": "3", "rotation": 270, "x": 1, "y": 1}, {"patternId": "Z", "rotation": 270, "x": 2, "y": 1}], "slot_sequence": ["LEFT", "BOTTOM"], "required_slots": ["LEFT", "BOTTOM"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C094\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): W -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=3, rotation=270, flipVertical=true\n- step 2: patternId=Z, rotation=270, flipVertical=true\n- allowed patternId values for this task: 3, Z, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C094"} +{"sample_id": "C095", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "E"], "observed_path_faces": [{"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C095_path_sequence.png"}, "metadata": {"level_id": 95, "name": "Reconstruct 095", "difficulty": 1, "move_count": 3, "tier": 1, "source_level_path": "levels/reconstruct/generated-095.json", "tier_label": "Difficulty 1"}, "description": "3-move reconstruct puzzle", "net_faces": [{"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["U", "7", "plus", "arrow_right", "E", "U"], "start_x": 2, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "U", "rotation": 90}, "BOTTOM": {"patternId": "U", "rotation": 180}, "FRONT": {"patternId": "7", "rotation": 90}, "BACK": {"patternId": "arrow_right", "rotation": 0}, "LEFT": {"patternId": "E", "rotation": 90}, "RIGHT": {"patternId": "plus", "rotation": 180}}, "bottom_faces": [{"patternId": "U", "rotation": 180, "x": 2, "y": 2}, {"patternId": "arrow_right", "rotation": 180, "x": 2, "y": 1}, {"patternId": "E", "rotation": 270, "x": 1, "y": 1}, {"patternId": "arrow_right", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["BACK", "LEFT", "BACK"], "required_slots": ["BACK", "LEFT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_right", "rotation": 180}, "LEFT": {"patternId": "E", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_right", "rotation": 180}, "LEFT": {"patternId": "E", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C095\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_right, rotation=180, flipVertical=true\n- step 2: patternId=E, rotation=270, flipVertical=true\n- step 3: patternId=arrow_right, rotation=180, flipVertical=true\n- allowed patternId values for this task: arrow_right, E, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C095"} +{"sample_id": "C096", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E"], "observed_path_faces": [{"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C096_path_sequence.png"}, "metadata": {"level_id": 96, "name": "Reconstruct 096", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-096.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["L", "triangle", "V", "square", "4", "A"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 3, "true_solution_faces": {"TOP": {"patternId": "L", "rotation": 270}, "BOTTOM": {"patternId": "A", "rotation": 0}, "FRONT": {"patternId": "triangle", "rotation": 0}, "BACK": {"patternId": "square", "rotation": 180}, "LEFT": {"patternId": "4", "rotation": 270}, "RIGHT": {"patternId": "V", "rotation": 0}}, "bottom_faces": [{"patternId": "A", "rotation": 0, "x": 1, "y": 1}, {"patternId": "V", "rotation": 90, "x": 2, "y": 1}, {"patternId": "L", "rotation": 90, "x": 3, "y": 1}], "slot_sequence": ["RIGHT", "TOP"], "required_slots": ["RIGHT", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "L", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "V", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "L", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "V", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C096\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=V, rotation=90, flipVertical=true\n- step 2: patternId=L, rotation=90, flipVertical=true\n- allowed patternId values for this task: V, L, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C096"} +{"sample_id": "C097", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W"], "observed_path_faces": [{"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C097_path_sequence.png"}, "metadata": {"level_id": 97, "name": "Reconstruct 097", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-097.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["3", "arrow_down", "Q", "X", "I", "K"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 3, "true_solution_faces": {"TOP": {"patternId": "3", "rotation": 0}, "BOTTOM": {"patternId": "K", "rotation": 90}, "FRONT": {"patternId": "arrow_down", "rotation": 180}, "BACK": {"patternId": "X", "rotation": 0}, "LEFT": {"patternId": "I", "rotation": 90}, "RIGHT": {"patternId": "Q", "rotation": 0}}, "bottom_faces": [{"patternId": "K", "rotation": 90, "x": 3, "y": 1}, {"patternId": "I", "rotation": 0, "x": 2, "y": 1}, {"patternId": "3", "rotation": 180, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "TOP"], "required_slots": ["LEFT", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "3", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "I", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "3", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "I", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C097\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=I, rotation=0, flipVertical=true\n- step 2: patternId=3, rotation=180, flipVertical=true\n- allowed patternId values for this task: I, 3, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C097"} +{"sample_id": "C098", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E"], "observed_path_faces": [{"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C098_path_sequence.png"}, "metadata": {"level_id": 98, "name": "Reconstruct 098", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-098.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["circle", "I", "S", "triangle", "heart", "A"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 3, "true_solution_faces": {"TOP": {"patternId": "circle", "rotation": 90}, "BOTTOM": {"patternId": "A", "rotation": 270}, "FRONT": {"patternId": "I", "rotation": 0}, "BACK": {"patternId": "triangle", "rotation": 270}, "LEFT": {"patternId": "heart", "rotation": 90}, "RIGHT": {"patternId": "S", "rotation": 270}}, "bottom_faces": [{"patternId": "A", "rotation": 270, "x": 1, "y": 1}, {"patternId": "S", "rotation": 0, "x": 2, "y": 1}, {"patternId": "circle", "rotation": 270, "x": 3, "y": 1}], "slot_sequence": ["RIGHT", "TOP"], "required_slots": ["RIGHT", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "circle", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C098\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=S, rotation=0, flipVertical=true\n- step 2: patternId=circle, rotation=270, flipVertical=true\n- allowed patternId values for this task: S, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C098"} +{"sample_id": "C099", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S"], "observed_path_faces": [{"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C099_path_sequence.png"}, "metadata": {"level_id": 99, "name": "Reconstruct 099", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-099.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["6", "G", "2", "arrow_down", "arrow_left", "Z"], "start_x": 1, "start_y": 1, "grid_width": 3, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "6", "rotation": 90}, "BOTTOM": {"patternId": "Z", "rotation": 90}, "FRONT": {"patternId": "G", "rotation": 180}, "BACK": {"patternId": "arrow_down", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 270}, "RIGHT": {"patternId": "2", "rotation": 180}}, "bottom_faces": [{"patternId": "Z", "rotation": 90, "x": 1, "y": 1}, {"patternId": "G", "rotation": 180, "x": 1, "y": 2}, {"patternId": "6", "rotation": 90, "x": 1, "y": 3}], "slot_sequence": ["FRONT", "TOP"], "required_slots": ["FRONT", "TOP"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "6", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "G", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "G", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C099\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=G, rotation=180, flipVertical=true\n- step 2: patternId=6, rotation=90, flipVertical=true\n- allowed patternId values for this task: G, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C099"} +{"sample_id": "C100", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E"], "observed_path_faces": [{"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C100_path_sequence.png"}, "metadata": {"level_id": 100, "name": "Reconstruct 100", "difficulty": 1, "move_count": 2, "tier": 1, "source_level_path": "levels/reconstruct/generated-100.json", "tier_label": "Difficulty 1"}, "description": "2-move reconstruct puzzle", "net_faces": [{"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["W", "1", "arrow_right", "star", "D", "star"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "W", "rotation": 90}, "BOTTOM": {"patternId": "star", "rotation": 90}, "FRONT": {"patternId": "1", "rotation": 90}, "BACK": {"patternId": "star", "rotation": 90}, "LEFT": {"patternId": "D", "rotation": 270}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}}, "bottom_faces": [{"patternId": "star", "rotation": 90, "x": 1, "y": 2}, {"patternId": "star", "rotation": 270, "x": 1, "y": 1}, {"patternId": "arrow_right", "rotation": 90, "x": 2, "y": 1}], "slot_sequence": ["BACK", "RIGHT"], "required_slots": ["BACK", "RIGHT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C100\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=star, rotation=270, flipVertical=true\n- step 2: patternId=arrow_right, rotation=90, flipVertical=true\n- allowed patternId values for this task: star, arrow_right, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C100"} +{"sample_id": "C101", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "E", "N"], "observed_path_faces": [{"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C101_path_sequence.png"}, "metadata": {"level_id": 101, "name": "Reconstruct 101", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-101.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_left", "W", "W", "circle", "U", "Z"], "start_x": 2, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "arrow_left", "rotation": 0}, "BOTTOM": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "W", "rotation": 180}, "BACK": {"patternId": "circle", "rotation": 90}, "LEFT": {"patternId": "U", "rotation": 0}, "RIGHT": {"patternId": "W", "rotation": 180}}, "bottom_faces": [{"patternId": "Z", "rotation": 270, "x": 2, "y": 3}, {"patternId": "U", "rotation": 270, "x": 1, "y": 3}, {"patternId": "circle", "rotation": 0, "x": 1, "y": 2}, {"patternId": "Z", "rotation": 0, "x": 2, "y": 2}, {"patternId": "W", "rotation": 0, "x": 2, "y": 1}], "slot_sequence": ["LEFT", "BACK", "BOTTOM", "RIGHT"], "required_slots": ["LEFT", "BACK", "BOTTOM", "RIGHT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 270}, "LEFT": {"patternId": "U", "rotation": 90}, "RIGHT": {"patternId": "W", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 270}, "LEFT": {"patternId": "U", "rotation": 90}, "RIGHT": {"patternId": "W", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C101\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=U, rotation=270, flipVertical=true\n- step 2: patternId=circle, rotation=0, flipVertical=true\n- step 3: patternId=Z, rotation=0, flipVertical=true\n- step 4: patternId=W, rotation=0, flipVertical=true\n- allowed patternId values for this task: U, circle, Z, W, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C101"} +{"sample_id": "C102", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> W -> S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "W", "S", "N"], "observed_path_faces": [{"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C102_path_sequence.png"}, "metadata": {"level_id": 102, "name": "Reconstruct 102", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-102.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["H", "V", "arrow_right", "7", "8", "5"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "H", "rotation": 180}, "BOTTOM": {"patternId": "5", "rotation": 180}, "FRONT": {"patternId": "V", "rotation": 0}, "BACK": {"patternId": "7", "rotation": 90}, "LEFT": {"patternId": "8", "rotation": 270}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}}, "bottom_faces": [{"patternId": "5", "rotation": 180, "x": 1, "y": 2}, {"patternId": "7", "rotation": 270, "x": 1, "y": 1}, {"patternId": "arrow_right", "rotation": 90, "x": 2, "y": 1}, {"patternId": "7", "rotation": 270, "x": 1, "y": 1}, {"patternId": "5", "rotation": 180, "x": 1, "y": 2}, {"patternId": "7", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["BACK", "RIGHT", "BACK", "BOTTOM", "BACK"], "required_slots": ["BACK", "RIGHT", "BOTTOM"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "5", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "7", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "5", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "7", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C102\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> W -> S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=7, rotation=270, flipVertical=true\n- step 2: patternId=arrow_right, rotation=90, flipVertical=true\n- step 3: patternId=7, rotation=270, flipVertical=true\n- step 4: patternId=5, rotation=180, flipVertical=true\n- step 5: patternId=7, rotation=270, flipVertical=true\n- allowed patternId values for this task: 7, arrow_right, 5, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C102"} +{"sample_id": "C103", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> W -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "W", "N", "W"], "observed_path_faces": [{"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C103_path_sequence.png"}, "metadata": {"level_id": 103, "name": "Reconstruct 103", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-103.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["R", "T", "R", "X", "V", "H"], "start_x": 2, "start_y": 3, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "R", "rotation": 180}, "BOTTOM": {"patternId": "H", "rotation": 90}, "FRONT": {"patternId": "T", "rotation": 270}, "BACK": {"patternId": "X", "rotation": 0}, "LEFT": {"patternId": "V", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 0}}, "bottom_faces": [{"patternId": "H", "rotation": 90, "x": 2, "y": 3}, {"patternId": "X", "rotation": 180, "x": 2, "y": 2}, {"patternId": "R", "rotation": 180, "x": 3, "y": 2}, {"patternId": "X", "rotation": 180, "x": 2, "y": 2}, {"patternId": "R", "rotation": 180, "x": 2, "y": 1}, {"patternId": "V", "rotation": 90, "x": 1, "y": 1}], "slot_sequence": ["BACK", "RIGHT", "BACK", "TOP", "LEFT"], "required_slots": ["BACK", "RIGHT", "TOP", "LEFT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "R", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "X", "rotation": 180}, "LEFT": {"patternId": "V", "rotation": 90}, "RIGHT": {"patternId": "R", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "R", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "X", "rotation": 180}, "LEFT": {"patternId": "V", "rotation": 90}, "RIGHT": {"patternId": "R", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C103\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> W -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=X, rotation=180, flipVertical=true\n- step 2: patternId=R, rotation=180, flipVertical=true\n- step 3: patternId=X, rotation=180, flipVertical=true\n- step 4: patternId=R, rotation=180, flipVertical=true\n- step 5: patternId=V, rotation=90, flipVertical=true\n- allowed patternId values for this task: X, R, V, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C103"} +{"sample_id": "C104", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "N", "E"], "observed_path_faces": [{"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C104_path_sequence.png"}, "metadata": {"level_id": 104, "name": "Reconstruct 104", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-104.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["M", "C", "5", "R", "S", "A"], "start_x": 2, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "M", "rotation": 270}, "BOTTOM": {"patternId": "A", "rotation": 180}, "FRONT": {"patternId": "C", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 270}, "LEFT": {"patternId": "S", "rotation": 90}, "RIGHT": {"patternId": "5", "rotation": 90}}, "bottom_faces": [{"patternId": "A", "rotation": 180, "x": 2, "y": 3}, {"patternId": "R", "rotation": 90, "x": 2, "y": 2}, {"patternId": "S", "rotation": 270, "x": 1, "y": 2}, {"patternId": "M", "rotation": 0, "x": 1, "y": 1}, {"patternId": "R", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["BACK", "LEFT", "TOP", "BACK"], "required_slots": ["BACK", "LEFT", "TOP"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "M", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 90}, "LEFT": {"patternId": "S", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 90}, "LEFT": {"patternId": "S", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C104\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=R, rotation=90, flipVertical=true\n- step 2: patternId=S, rotation=270, flipVertical=true\n- step 3: patternId=M, rotation=0, flipVertical=true\n- step 4: patternId=R, rotation=180, flipVertical=true\n- allowed patternId values for this task: R, S, M, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C104"} +{"sample_id": "C105", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> W -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "W", "E"], "observed_path_faces": [{"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C105_path_sequence.png"}, "metadata": {"level_id": 105, "name": "Reconstruct 105", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-105.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["V", "L", "arrow_left", "Y", "8", "4"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "V", "rotation": 270}, "BOTTOM": {"patternId": "4", "rotation": 180}, "FRONT": {"patternId": "L", "rotation": 90}, "BACK": {"patternId": "Y", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 90}}, "bottom_faces": [{"patternId": "4", "rotation": 180, "x": 3, "y": 1}, {"patternId": "8", "rotation": 270, "x": 2, "y": 1}, {"patternId": "L", "rotation": 0, "x": 2, "y": 2}, {"patternId": "V", "rotation": 180, "x": 1, "y": 2}, {"patternId": "L", "rotation": 0, "x": 2, "y": 2}], "slot_sequence": ["LEFT", "FRONT", "TOP", "FRONT"], "required_slots": ["LEFT", "FRONT", "TOP"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "V", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "L", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "V", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "L", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C105\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> W -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=8, rotation=270, flipVertical=true\n- step 2: patternId=L, rotation=0, flipVertical=true\n- step 3: patternId=V, rotation=180, flipVertical=true\n- step 4: patternId=L, rotation=0, flipVertical=true\n- allowed patternId values for this task: 8, L, V, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C105"} +{"sample_id": "C106", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> W -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "W", "N", "N"], "observed_path_faces": [{"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C106_path_sequence.png"}, "metadata": {"level_id": 106, "name": "Reconstruct 106", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-106.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["M", "5", "L", "star", "diamond", "U"], "start_x": 1, "start_y": 4, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "M", "rotation": 90}, "BOTTOM": {"patternId": "U", "rotation": 270}, "FRONT": {"patternId": "5", "rotation": 270}, "BACK": {"patternId": "star", "rotation": 270}, "LEFT": {"patternId": "diamond", "rotation": 180}, "RIGHT": {"patternId": "L", "rotation": 270}}, "bottom_faces": [{"patternId": "U", "rotation": 270, "x": 1, "y": 4}, {"patternId": "L", "rotation": 0, "x": 2, "y": 4}, {"patternId": "star", "rotation": 0, "x": 2, "y": 3}, {"patternId": "U", "rotation": 180, "x": 1, "y": 3}, {"patternId": "diamond", "rotation": 0, "x": 1, "y": 2}, {"patternId": "M", "rotation": 180, "x": 1, "y": 1}], "slot_sequence": ["RIGHT", "BACK", "BOTTOM", "LEFT", "TOP"], "required_slots": ["RIGHT", "BACK", "BOTTOM", "LEFT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "M", "rotation": 90}, "BOTTOM": {"patternId": "U", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 90}, "LEFT": {"patternId": "diamond", "rotation": 270}, "RIGHT": {"patternId": "L", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 90}, "BOTTOM": {"patternId": "U", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 90}, "LEFT": {"patternId": "diamond", "rotation": 270}, "RIGHT": {"patternId": "L", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C106\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> W -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=L, rotation=0, flipVertical=true\n- step 2: patternId=star, rotation=0, flipVertical=true\n- step 3: patternId=U, rotation=180, flipVertical=true\n- step 4: patternId=diamond, rotation=0, flipVertical=true\n- step 5: patternId=M, rotation=180, flipVertical=true\n- allowed patternId values for this task: L, star, U, diamond, M, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C106"} +{"sample_id": "C107", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> E -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "E", "N", "E"], "observed_path_faces": [{"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C107_path_sequence.png"}, "metadata": {"level_id": 107, "name": "Reconstruct 107", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-107.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["O", "H", "6", "Z", "X", "8"], "start_x": 2, "start_y": 3, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "8", "rotation": 90}, "FRONT": {"patternId": "H", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "X", "rotation": 270}, "RIGHT": {"patternId": "6", "rotation": 0}}, "bottom_faces": [{"patternId": "8", "rotation": 90, "x": 2, "y": 3}, {"patternId": "X", "rotation": 180, "x": 1, "y": 3}, {"patternId": "Z", "rotation": 180, "x": 1, "y": 2}, {"patternId": "8", "rotation": 180, "x": 2, "y": 2}, {"patternId": "6", "rotation": 180, "x": 2, "y": 1}, {"patternId": "H", "rotation": 0, "x": 3, "y": 1}], "slot_sequence": ["LEFT", "BACK", "BOTTOM", "RIGHT", "FRONT"], "required_slots": ["LEFT", "BACK", "BOTTOM", "RIGHT", "FRONT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 90}, "FRONT": {"patternId": "H", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "X", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 90}, "FRONT": {"patternId": "H", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "X", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C107\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> E -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=X, rotation=180, flipVertical=true\n- step 2: patternId=Z, rotation=180, flipVertical=true\n- step 3: patternId=8, rotation=180, flipVertical=true\n- step 4: patternId=6, rotation=180, flipVertical=true\n- step 5: patternId=H, rotation=0, flipVertical=true\n- allowed patternId values for this task: X, Z, 8, 6, H, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C107"} +{"sample_id": "C108", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> W -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "W", "N", "N"], "observed_path_faces": [{"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C108_path_sequence.png"}, "metadata": {"level_id": 108, "name": "Reconstruct 108", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-108.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["square", "I", "smile", "arrow_left", "U", "B"], "start_x": 1, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "square", "rotation": 270}, "BOTTOM": {"patternId": "B", "rotation": 180}, "FRONT": {"patternId": "I", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 0}, "LEFT": {"patternId": "U", "rotation": 270}, "RIGHT": {"patternId": "smile", "rotation": 0}}, "bottom_faces": [{"patternId": "B", "rotation": 180, "x": 1, "y": 3}, {"patternId": "smile", "rotation": 90, "x": 2, "y": 3}, {"patternId": "B", "rotation": 180, "x": 1, "y": 3}, {"patternId": "arrow_left", "rotation": 180, "x": 1, "y": 2}, {"patternId": "square", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["RIGHT", "BOTTOM", "BACK", "TOP"], "required_slots": ["RIGHT", "BOTTOM", "BACK", "TOP"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "square", "rotation": 270}, "BOTTOM": {"patternId": "B", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "smile", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "square", "rotation": 270}, "BOTTOM": {"patternId": "B", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "smile", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C108\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> W -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=smile, rotation=90, flipVertical=true\n- step 2: patternId=B, rotation=180, flipVertical=true\n- step 3: patternId=arrow_left, rotation=180, flipVertical=true\n- step 4: patternId=square, rotation=270, flipVertical=true\n- allowed patternId values for this task: smile, B, arrow_left, square, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C108"} +{"sample_id": "C109", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "S", "S"], "observed_path_faces": [{"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C109_path_sequence.png"}, "metadata": {"level_id": 109, "name": "Reconstruct 109", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-109.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["9", "B", "1", "2", "N", "5"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "9", "rotation": 0}, "BOTTOM": {"patternId": "5", "rotation": 180}, "FRONT": {"patternId": "B", "rotation": 180}, "BACK": {"patternId": "2", "rotation": 90}, "LEFT": {"patternId": "N", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 0}}, "bottom_faces": [{"patternId": "5", "rotation": 180, "x": 1, "y": 1}, {"patternId": "1", "rotation": 90, "x": 2, "y": 1}, {"patternId": "9", "rotation": 180, "x": 3, "y": 1}, {"patternId": "B", "rotation": 0, "x": 3, "y": 2}, {"patternId": "5", "rotation": 0, "x": 3, "y": 3}], "slot_sequence": ["RIGHT", "TOP", "FRONT", "BOTTOM"], "required_slots": ["RIGHT", "TOP", "FRONT", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "9", "rotation": 0}, "BOTTOM": {"patternId": "5", "rotation": 180}, "FRONT": {"patternId": "B", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "9", "rotation": 0}, "BOTTOM": {"patternId": "5", "rotation": 180}, "FRONT": {"patternId": "B", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C109\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=1, rotation=90, flipVertical=true\n- step 2: patternId=9, rotation=180, flipVertical=true\n- step 3: patternId=B, rotation=0, flipVertical=true\n- step 4: patternId=5, rotation=0, flipVertical=true\n- allowed patternId values for this task: 1, 9, B, 5, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C109"} +{"sample_id": "C110", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "W", "E"], "observed_path_faces": [{"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C110_path_sequence.png"}, "metadata": {"level_id": 110, "name": "Reconstruct 110", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-110.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["T", "arrow_right", "T", "W", "smile", "J"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "T", "rotation": 90}, "BOTTOM": {"patternId": "J", "rotation": 90}, "FRONT": {"patternId": "arrow_right", "rotation": 0}, "BACK": {"patternId": "W", "rotation": 180}, "LEFT": {"patternId": "smile", "rotation": 0}, "RIGHT": {"patternId": "T", "rotation": 0}}, "bottom_faces": [{"patternId": "J", "rotation": 90, "x": 1, "y": 1}, {"patternId": "T", "rotation": 90, "x": 2, "y": 1}, {"patternId": "arrow_right", "rotation": 90, "x": 2, "y": 2}, {"patternId": "J", "rotation": 180, "x": 1, "y": 2}, {"patternId": "arrow_right", "rotation": 90, "x": 2, "y": 2}], "slot_sequence": ["RIGHT", "FRONT", "BOTTOM", "FRONT"], "required_slots": ["RIGHT", "FRONT", "BOTTOM"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "J", "rotation": 90}, "FRONT": {"patternId": "arrow_right", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "T", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "J", "rotation": 90}, "FRONT": {"patternId": "arrow_right", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "T", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C110\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=T, rotation=90, flipVertical=true\n- step 2: patternId=arrow_right, rotation=90, flipVertical=true\n- step 3: patternId=J, rotation=180, flipVertical=true\n- step 4: patternId=arrow_right, rotation=90, flipVertical=true\n- allowed patternId values for this task: T, arrow_right, J, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C110"} +{"sample_id": "C111", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "W", "N"], "observed_path_faces": [{"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C111_path_sequence.png"}, "metadata": {"level_id": 111, "name": "Reconstruct 111", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-111.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["M", "Y", "diamond", "diamond", "H", "H"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "M", "rotation": 270}, "BOTTOM": {"patternId": "H", "rotation": 0}, "FRONT": {"patternId": "Y", "rotation": 0}, "BACK": {"patternId": "diamond", "rotation": 270}, "LEFT": {"patternId": "H", "rotation": 90}, "RIGHT": {"patternId": "diamond", "rotation": 90}}, "bottom_faces": [{"patternId": "H", "rotation": 0, "x": 1, "y": 1}, {"patternId": "diamond", "rotation": 180, "x": 2, "y": 1}, {"patternId": "Y", "rotation": 90, "x": 2, "y": 2}, {"patternId": "H", "rotation": 90, "x": 1, "y": 2}, {"patternId": "diamond", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["RIGHT", "FRONT", "BOTTOM", "RIGHT"], "required_slots": ["RIGHT", "FRONT", "BOTTOM"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "H", "rotation": 0}, "FRONT": {"patternId": "Y", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "diamond", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "H", "rotation": 0}, "FRONT": {"patternId": "Y", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "diamond", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C111\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=diamond, rotation=180, flipVertical=true\n- step 2: patternId=Y, rotation=90, flipVertical=true\n- step 3: patternId=H, rotation=90, flipVertical=true\n- step 4: patternId=diamond, rotation=270, flipVertical=true\n- allowed patternId values for this task: diamond, Y, H, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C111"} +{"sample_id": "C112", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "E", "N"], "observed_path_faces": [{"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C112_path_sequence.png"}, "metadata": {"level_id": 112, "name": "Reconstruct 112", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-112.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["P", "L", "S", "Q", "arrow_down", "arrow_down"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "P", "rotation": 270}, "BOTTOM": {"patternId": "arrow_down", "rotation": 180}, "FRONT": {"patternId": "L", "rotation": 90}, "BACK": {"patternId": "Q", "rotation": 270}, "LEFT": {"patternId": "arrow_down", "rotation": 180}, "RIGHT": {"patternId": "S", "rotation": 180}}, "bottom_faces": [{"patternId": "arrow_down", "rotation": 180, "x": 2, "y": 1}, {"patternId": "arrow_down", "rotation": 90, "x": 1, "y": 1}, {"patternId": "L", "rotation": 0, "x": 1, "y": 2}, {"patternId": "arrow_down", "rotation": 90, "x": 2, "y": 2}, {"patternId": "arrow_down", "rotation": 0, "x": 2, "y": 1}], "slot_sequence": ["LEFT", "FRONT", "BOTTOM", "LEFT"], "required_slots": ["LEFT", "FRONT", "BOTTOM"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_down", "rotation": 180}, "FRONT": {"patternId": "L", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_down", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_down", "rotation": 180}, "FRONT": {"patternId": "L", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_down", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C112\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_down, rotation=90, flipVertical=true\n- step 2: patternId=L, rotation=0, flipVertical=true\n- step 3: patternId=arrow_down, rotation=90, flipVertical=true\n- step 4: patternId=arrow_down, rotation=0, flipVertical=true\n- allowed patternId values for this task: arrow_down, L, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C112"} +{"sample_id": "C113", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> N -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "N", "E", "S"], "observed_path_faces": [{"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C113_path_sequence.png"}, "metadata": {"level_id": 113, "name": "Reconstruct 113", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-113.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["W", "smile", "Q", "arrow_down", "circle", "W"], "start_x": 2, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "W", "rotation": 270}, "BOTTOM": {"patternId": "W", "rotation": 90}, "FRONT": {"patternId": "smile", "rotation": 180}, "BACK": {"patternId": "arrow_down", "rotation": 90}, "LEFT": {"patternId": "circle", "rotation": 0}, "RIGHT": {"patternId": "Q", "rotation": 90}}, "bottom_faces": [{"patternId": "W", "rotation": 90, "x": 2, "y": 3}, {"patternId": "circle", "rotation": 270, "x": 1, "y": 3}, {"patternId": "arrow_down", "rotation": 0, "x": 1, "y": 2}, {"patternId": "Q", "rotation": 0, "x": 1, "y": 1}, {"patternId": "W", "rotation": 270, "x": 2, "y": 1}, {"patternId": "arrow_down", "rotation": 90, "x": 2, "y": 2}], "slot_sequence": ["LEFT", "BACK", "RIGHT", "BOTTOM", "BACK"], "required_slots": ["LEFT", "BACK", "RIGHT", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_down", "rotation": 270}, "LEFT": {"patternId": "circle", "rotation": 90}, "RIGHT": {"patternId": "Q", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_down", "rotation": 270}, "LEFT": {"patternId": "circle", "rotation": 90}, "RIGHT": {"patternId": "Q", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C113\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> N -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=circle, rotation=270, flipVertical=true\n- step 2: patternId=arrow_down, rotation=0, flipVertical=true\n- step 3: patternId=Q, rotation=0, flipVertical=true\n- step 4: patternId=W, rotation=270, flipVertical=true\n- step 5: patternId=arrow_down, rotation=90, flipVertical=true\n- allowed patternId values for this task: circle, arrow_down, Q, W, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C113"} +{"sample_id": "C114", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> E -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "E", "N", "N"], "observed_path_faces": [{"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C114_path_sequence.png"}, "metadata": {"level_id": 114, "name": "Reconstruct 114", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-114.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["W", "Q", "smile", "D", "T", "C"], "start_x": 2, "start_y": 2, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "W", "rotation": 0}, "BOTTOM": {"patternId": "C", "rotation": 270}, "FRONT": {"patternId": "Q", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 180}, "LEFT": {"patternId": "T", "rotation": 270}, "RIGHT": {"patternId": "smile", "rotation": 90}}, "bottom_faces": [{"patternId": "C", "rotation": 270, "x": 2, "y": 2}, {"patternId": "T", "rotation": 180, "x": 1, "y": 2}, {"patternId": "Q", "rotation": 270, "x": 1, "y": 3}, {"patternId": "C", "rotation": 180, "x": 2, "y": 3}, {"patternId": "T", "rotation": 90, "x": 2, "y": 2}, {"patternId": "W", "rotation": 90, "x": 2, "y": 1}], "slot_sequence": ["LEFT", "FRONT", "BOTTOM", "LEFT", "TOP"], "required_slots": ["LEFT", "FRONT", "BOTTOM", "TOP"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "W", "rotation": 0}, "BOTTOM": {"patternId": "C", "rotation": 270}, "FRONT": {"patternId": "Q", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "T", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "W", "rotation": 0}, "BOTTOM": {"patternId": "C", "rotation": 270}, "FRONT": {"patternId": "Q", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "T", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C114\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> E -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=T, rotation=180, flipVertical=true\n- step 2: patternId=Q, rotation=270, flipVertical=true\n- step 3: patternId=C, rotation=180, flipVertical=true\n- step 4: patternId=T, rotation=90, flipVertical=true\n- step 5: patternId=W, rotation=90, flipVertical=true\n- allowed patternId values for this task: T, Q, C, W, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C114"} +{"sample_id": "C115", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> N -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "N", "S"], "observed_path_faces": [{"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C115_path_sequence.png"}, "metadata": {"level_id": 115, "name": "Reconstruct 115", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-115.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["heart", "circle", "plus", "V", "W", "R"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "heart", "rotation": 270}, "BOTTOM": {"patternId": "R", "rotation": 180}, "FRONT": {"patternId": "circle", "rotation": 90}, "BACK": {"patternId": "V", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "plus", "rotation": 90}}, "bottom_faces": [{"patternId": "R", "rotation": 180, "x": 1, "y": 1}, {"patternId": "plus", "rotation": 180, "x": 2, "y": 1}, {"patternId": "circle", "rotation": 180, "x": 2, "y": 2}, {"patternId": "plus", "rotation": 180, "x": 2, "y": 1}, {"patternId": "circle", "rotation": 180, "x": 2, "y": 2}], "slot_sequence": ["RIGHT", "FRONT", "RIGHT", "FRONT"], "required_slots": ["RIGHT", "FRONT"], "required_count": 2, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "circle", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "plus", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "circle", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "plus", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C115\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> N -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=plus, rotation=180, flipVertical=true\n- step 2: patternId=circle, rotation=180, flipVertical=true\n- step 3: patternId=plus, rotation=180, flipVertical=true\n- step 4: patternId=circle, rotation=180, flipVertical=true\n- allowed patternId values for this task: plus, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C115"} +{"sample_id": "C116", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> E -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "E", "N", "W"], "observed_path_faces": [{"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C116_path_sequence.png"}, "metadata": {"level_id": 116, "name": "Reconstruct 116", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-116.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["S", "D", "Z", "L", "2", "U"], "start_x": 1, "start_y": 3, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "S", "rotation": 90}, "BOTTOM": {"patternId": "U", "rotation": 90}, "FRONT": {"patternId": "D", "rotation": 0}, "BACK": {"patternId": "L", "rotation": 180}, "LEFT": {"patternId": "2", "rotation": 90}, "RIGHT": {"patternId": "Z", "rotation": 180}}, "bottom_faces": [{"patternId": "U", "rotation": 90, "x": 1, "y": 3}, {"patternId": "Z", "rotation": 270, "x": 2, "y": 3}, {"patternId": "L", "rotation": 270, "x": 2, "y": 2}, {"patternId": "S", "rotation": 0, "x": 3, "y": 2}, {"patternId": "2", "rotation": 90, "x": 3, "y": 1}, {"patternId": "L", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["RIGHT", "BACK", "TOP", "LEFT", "BACK"], "required_slots": ["RIGHT", "BACK", "TOP", "LEFT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "S", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "L", "rotation": 0}, "LEFT": {"patternId": "2", "rotation": 180}, "RIGHT": {"patternId": "Z", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "L", "rotation": 0}, "LEFT": {"patternId": "2", "rotation": 180}, "RIGHT": {"patternId": "Z", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C116\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> E -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Z, rotation=270, flipVertical=true\n- step 2: patternId=L, rotation=270, flipVertical=true\n- step 3: patternId=S, rotation=0, flipVertical=true\n- step 4: patternId=2, rotation=90, flipVertical=true\n- step 5: patternId=L, rotation=180, flipVertical=true\n- allowed patternId values for this task: Z, L, S, 2, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C116"} +{"sample_id": "C117", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> N -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "N", "N", "N"], "observed_path_faces": [{"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C117_path_sequence.png"}, "metadata": {"level_id": 117, "name": "Reconstruct 117", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-117.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["8", "O", "Z", "W", "L", "1"], "start_x": 1, "start_y": 3, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "8", "rotation": 90}, "BOTTOM": {"patternId": "1", "rotation": 90}, "FRONT": {"patternId": "O", "rotation": 0}, "BACK": {"patternId": "W", "rotation": 90}, "LEFT": {"patternId": "L", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 90}}, "bottom_faces": [{"patternId": "1", "rotation": 90, "x": 1, "y": 3}, {"patternId": "O", "rotation": 0, "x": 1, "y": 4}, {"patternId": "Z", "rotation": 90, "x": 2, "y": 4}, {"patternId": "1", "rotation": 0, "x": 2, "y": 3}, {"patternId": "L", "rotation": 180, "x": 2, "y": 2}, {"patternId": "8", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["FRONT", "RIGHT", "BOTTOM", "LEFT", "TOP"], "required_slots": ["FRONT", "RIGHT", "BOTTOM", "LEFT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "8", "rotation": 90}, "BOTTOM": {"patternId": "1", "rotation": 90}, "FRONT": {"patternId": "O", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "L", "rotation": 90}, "RIGHT": {"patternId": "Z", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "8", "rotation": 90}, "BOTTOM": {"patternId": "1", "rotation": 90}, "FRONT": {"patternId": "O", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "L", "rotation": 90}, "RIGHT": {"patternId": "Z", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C117\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> N -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=O, rotation=0, flipVertical=true\n- step 2: patternId=Z, rotation=90, flipVertical=true\n- step 3: patternId=1, rotation=0, flipVertical=true\n- step 4: patternId=L, rotation=180, flipVertical=true\n- step 5: patternId=8, rotation=180, flipVertical=true\n- allowed patternId values for this task: O, Z, 1, L, 8, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C117"} +{"sample_id": "C118", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "W", "N", "N"], "observed_path_faces": [{"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C118_path_sequence.png"}, "metadata": {"level_id": 118, "name": "Reconstruct 118", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-118.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["F", "W", "4", "L", "A", "D"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "F", "rotation": 180}, "BOTTOM": {"patternId": "D", "rotation": 0}, "FRONT": {"patternId": "W", "rotation": 270}, "BACK": {"patternId": "L", "rotation": 0}, "LEFT": {"patternId": "A", "rotation": 90}, "RIGHT": {"patternId": "4", "rotation": 180}}, "bottom_faces": [{"patternId": "D", "rotation": 0, "x": 1, "y": 2}, {"patternId": "4", "rotation": 270, "x": 2, "y": 2}, {"patternId": "W", "rotation": 0, "x": 2, "y": 3}, {"patternId": "D", "rotation": 90, "x": 1, "y": 3}, {"patternId": "4", "rotation": 0, "x": 1, "y": 2}, {"patternId": "F", "rotation": 90, "x": 1, "y": 1}], "slot_sequence": ["RIGHT", "FRONT", "BOTTOM", "RIGHT", "TOP"], "required_slots": ["RIGHT", "FRONT", "BOTTOM", "TOP"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "F", "rotation": 180}, "BOTTOM": {"patternId": "D", "rotation": 0}, "FRONT": {"patternId": "W", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "4", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "F", "rotation": 180}, "BOTTOM": {"patternId": "D", "rotation": 0}, "FRONT": {"patternId": "W", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "4", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C118\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=4, rotation=270, flipVertical=true\n- step 2: patternId=W, rotation=0, flipVertical=true\n- step 3: patternId=D, rotation=90, flipVertical=true\n- step 4: patternId=4, rotation=0, flipVertical=true\n- step 5: patternId=F, rotation=90, flipVertical=true\n- allowed patternId values for this task: 4, W, D, F, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C118"} +{"sample_id": "C119", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "E", "E"], "observed_path_faces": [{"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C119_path_sequence.png"}, "metadata": {"level_id": 119, "name": "Reconstruct 119", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-119.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["8", "G", "N", "W", "I", "G"], "start_x": 1, "start_y": 1, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "8", "rotation": 180}, "BOTTOM": {"patternId": "G", "rotation": 0}, "FRONT": {"patternId": "G", "rotation": 270}, "BACK": {"patternId": "W", "rotation": 90}, "LEFT": {"patternId": "I", "rotation": 0}, "RIGHT": {"patternId": "N", "rotation": 180}}, "bottom_faces": [{"patternId": "G", "rotation": 0, "x": 1, "y": 1}, {"patternId": "N", "rotation": 270, "x": 2, "y": 1}, {"patternId": "G", "rotation": 0, "x": 2, "y": 2}, {"patternId": "8", "rotation": 270, "x": 3, "y": 2}, {"patternId": "W", "rotation": 0, "x": 4, "y": 2}], "slot_sequence": ["RIGHT", "FRONT", "TOP", "BACK"], "required_slots": ["RIGHT", "FRONT", "TOP", "BACK"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "8", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "G", "rotation": 270}, "BACK": {"patternId": "W", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "N", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "8", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "G", "rotation": 270}, "BACK": {"patternId": "W", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "N", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C119\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=N, rotation=270, flipVertical=true\n- step 2: patternId=G, rotation=0, flipVertical=true\n- step 3: patternId=8, rotation=270, flipVertical=true\n- step 4: patternId=W, rotation=0, flipVertical=true\n- allowed patternId values for this task: N, G, 8, W, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C119"} +{"sample_id": "C120", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> W -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "W", "E", "S"], "observed_path_faces": [{"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C120_path_sequence.png"}, "metadata": {"level_id": 120, "name": "Reconstruct 120", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-120.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["plus", "6", "P", "V", "O", "K"], "start_x": 2, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "plus", "rotation": 90}, "BOTTOM": {"patternId": "K", "rotation": 90}, "FRONT": {"patternId": "6", "rotation": 270}, "BACK": {"patternId": "V", "rotation": 90}, "LEFT": {"patternId": "O", "rotation": 0}, "RIGHT": {"patternId": "P", "rotation": 180}}, "bottom_faces": [{"patternId": "K", "rotation": 90, "x": 2, "y": 3}, {"patternId": "V", "rotation": 270, "x": 2, "y": 2}, {"patternId": "plus", "rotation": 90, "x": 2, "y": 1}, {"patternId": "O", "rotation": 90, "x": 1, "y": 1}, {"patternId": "plus", "rotation": 90, "x": 2, "y": 1}, {"patternId": "V", "rotation": 270, "x": 2, "y": 2}], "slot_sequence": ["BACK", "TOP", "LEFT", "TOP", "BACK"], "required_slots": ["BACK", "TOP", "LEFT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "plus", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "V", "rotation": 270}, "LEFT": {"patternId": "O", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "plus", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "V", "rotation": 270}, "LEFT": {"patternId": "O", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C120\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> W -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=V, rotation=270, flipVertical=true\n- step 2: patternId=plus, rotation=90, flipVertical=true\n- step 3: patternId=O, rotation=90, flipVertical=true\n- step 4: patternId=plus, rotation=90, flipVertical=true\n- step 5: patternId=V, rotation=270, flipVertical=true\n- allowed patternId values for this task: V, plus, O, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C120"} +{"sample_id": "C121", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> N -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "N", "E", "E"], "observed_path_faces": [{"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C121_path_sequence.png"}, "metadata": {"level_id": 121, "name": "Reconstruct 121", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-121.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["A", "diamond", "S", "G", "V", "9"], "start_x": 1, "start_y": 2, "grid_width": 7, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "A", "rotation": 90}, "BOTTOM": {"patternId": "9", "rotation": 270}, "FRONT": {"patternId": "diamond", "rotation": 180}, "BACK": {"patternId": "G", "rotation": 0}, "LEFT": {"patternId": "V", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 90}}, "bottom_faces": [{"patternId": "9", "rotation": 270, "x": 1, "y": 2}, {"patternId": "S", "rotation": 180, "x": 2, "y": 2}, {"patternId": "A", "rotation": 270, "x": 3, "y": 2}, {"patternId": "G", "rotation": 0, "x": 3, "y": 1}, {"patternId": "V", "rotation": 0, "x": 4, "y": 1}, {"patternId": "diamond", "rotation": 180, "x": 5, "y": 1}], "slot_sequence": ["RIGHT", "TOP", "BACK", "LEFT", "FRONT"], "required_slots": ["RIGHT", "TOP", "BACK", "LEFT", "FRONT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "A", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 180}, "BACK": {"patternId": "G", "rotation": 180}, "LEFT": {"patternId": "V", "rotation": 90}, "RIGHT": {"patternId": "S", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "A", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 180}, "BACK": {"patternId": "G", "rotation": 180}, "LEFT": {"patternId": "V", "rotation": 90}, "RIGHT": {"patternId": "S", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C121\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> N -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=S, rotation=180, flipVertical=true\n- step 2: patternId=A, rotation=270, flipVertical=true\n- step 3: patternId=G, rotation=0, flipVertical=true\n- step 4: patternId=V, rotation=0, flipVertical=true\n- step 5: patternId=diamond, rotation=180, flipVertical=true\n- allowed patternId values for this task: S, A, G, V, diamond, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C121"} +{"sample_id": "C122", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> E -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "E", "N", "W"], "observed_path_faces": [{"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C122_path_sequence.png"}, "metadata": {"level_id": 122, "name": "Reconstruct 122", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-122.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["T", "3", "8", "1", "A", "V"], "start_x": 1, "start_y": 2, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "T", "rotation": 0}, "BOTTOM": {"patternId": "V", "rotation": 90}, "FRONT": {"patternId": "3", "rotation": 270}, "BACK": {"patternId": "1", "rotation": 0}, "LEFT": {"patternId": "A", "rotation": 90}, "RIGHT": {"patternId": "8", "rotation": 180}}, "bottom_faces": [{"patternId": "V", "rotation": 90, "x": 1, "y": 2}, {"patternId": "8", "rotation": 270, "x": 2, "y": 2}, {"patternId": "T", "rotation": 180, "x": 3, "y": 2}, {"patternId": "A", "rotation": 0, "x": 4, "y": 2}, {"patternId": "1", "rotation": 270, "x": 4, "y": 1}, {"patternId": "T", "rotation": 90, "x": 3, "y": 1}], "slot_sequence": ["RIGHT", "TOP", "LEFT", "BACK", "TOP"], "required_slots": ["RIGHT", "TOP", "LEFT", "BACK"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "T", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "A", "rotation": 180}, "RIGHT": {"patternId": "8", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "T", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "A", "rotation": 180}, "RIGHT": {"patternId": "8", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C122\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> E -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=8, rotation=270, flipVertical=true\n- step 2: patternId=T, rotation=180, flipVertical=true\n- step 3: patternId=A, rotation=0, flipVertical=true\n- step 4: patternId=1, rotation=270, flipVertical=true\n- step 5: patternId=T, rotation=90, flipVertical=true\n- allowed patternId values for this task: 8, T, A, 1, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C122"} +{"sample_id": "C123", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "S", "S"], "observed_path_faces": [{"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C123_path_sequence.png"}, "metadata": {"level_id": 123, "name": "Reconstruct 123", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-123.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["6", "V", "S", "arrow_up", "diamond", "2"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "6", "rotation": 0}, "BOTTOM": {"patternId": "2", "rotation": 90}, "FRONT": {"patternId": "V", "rotation": 90}, "BACK": {"patternId": "arrow_up", "rotation": 270}, "LEFT": {"patternId": "diamond", "rotation": 90}, "RIGHT": {"patternId": "S", "rotation": 0}}, "bottom_faces": [{"patternId": "2", "rotation": 90, "x": 1, "y": 2}, {"patternId": "arrow_up", "rotation": 90, "x": 1, "y": 1}, {"patternId": "S", "rotation": 180, "x": 2, "y": 1}, {"patternId": "2", "rotation": 180, "x": 2, "y": 2}, {"patternId": "diamond", "rotation": 90, "x": 2, "y": 3}], "slot_sequence": ["BACK", "RIGHT", "BOTTOM", "LEFT"], "required_slots": ["BACK", "RIGHT", "BOTTOM", "LEFT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "2", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_up", "rotation": 90}, "LEFT": {"patternId": "diamond", "rotation": 180}, "RIGHT": {"patternId": "S", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "2", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_up", "rotation": 90}, "LEFT": {"patternId": "diamond", "rotation": 180}, "RIGHT": {"patternId": "S", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C123\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_up, rotation=90, flipVertical=true\n- step 2: patternId=S, rotation=180, flipVertical=true\n- step 3: patternId=2, rotation=180, flipVertical=true\n- step 4: patternId=diamond, rotation=90, flipVertical=true\n- allowed patternId values for this task: arrow_up, S, 2, diamond, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C123"} +{"sample_id": "C124", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> W -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "W", "W", "N"], "observed_path_faces": [{"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C124_path_sequence.png"}, "metadata": {"level_id": 124, "name": "Reconstruct 124", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-124.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Y", "P", "O", "circle", "arrow_left", "arrow_left"], "start_x": 4, "start_y": 1, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "Y", "rotation": 0}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "P", "rotation": 90}, "BACK": {"patternId": "circle", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 270}, "RIGHT": {"patternId": "O", "rotation": 0}}, "bottom_faces": [{"patternId": "arrow_left", "rotation": 0, "x": 4, "y": 1}, {"patternId": "P", "rotation": 90, "x": 4, "y": 2}, {"patternId": "arrow_left", "rotation": 270, "x": 3, "y": 2}, {"patternId": "circle", "rotation": 0, "x": 2, "y": 2}, {"patternId": "O", "rotation": 0, "x": 1, "y": 2}, {"patternId": "arrow_left", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["FRONT", "LEFT", "BACK", "RIGHT", "BOTTOM"], "required_slots": ["FRONT", "LEFT", "BACK", "RIGHT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "P", "rotation": 90}, "BACK": {"patternId": "circle", "rotation": 180}, "LEFT": {"patternId": "arrow_left", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "P", "rotation": 90}, "BACK": {"patternId": "circle", "rotation": 180}, "LEFT": {"patternId": "arrow_left", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C124\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> W -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=P, rotation=90, flipVertical=true\n- step 2: patternId=arrow_left, rotation=270, flipVertical=true\n- step 3: patternId=circle, rotation=0, flipVertical=true\n- step 4: patternId=O, rotation=0, flipVertical=true\n- step 5: patternId=arrow_left, rotation=270, flipVertical=true\n- allowed patternId values for this task: P, arrow_left, circle, O, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C124"} +{"sample_id": "C125", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> W -> W -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "W", "W", "E"], "observed_path_faces": [{"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C125_path_sequence.png"}, "metadata": {"level_id": 125, "name": "Reconstruct 125", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-125.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["square", "K", "D", "circle", "O", "arrow_right"], "start_x": 4, "start_y": 1, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "square", "rotation": 90}, "BOTTOM": {"patternId": "arrow_right", "rotation": 180}, "FRONT": {"patternId": "K", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 270}, "LEFT": {"patternId": "O", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 0}}, "bottom_faces": [{"patternId": "arrow_right", "rotation": 180, "x": 4, "y": 1}, {"patternId": "O", "rotation": 270, "x": 3, "y": 1}, {"patternId": "K", "rotation": 270, "x": 3, "y": 2}, {"patternId": "square", "rotation": 0, "x": 2, "y": 2}, {"patternId": "circle", "rotation": 0, "x": 1, "y": 2}, {"patternId": "square", "rotation": 0, "x": 2, "y": 2}], "slot_sequence": ["LEFT", "FRONT", "TOP", "BACK", "TOP"], "required_slots": ["LEFT", "FRONT", "TOP", "BACK"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "square", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "K", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 90}, "LEFT": {"patternId": "O", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "square", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "K", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 90}, "LEFT": {"patternId": "O", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C125\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> W -> W -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=O, rotation=270, flipVertical=true\n- step 2: patternId=K, rotation=270, flipVertical=true\n- step 3: patternId=square, rotation=0, flipVertical=true\n- step 4: patternId=circle, rotation=0, flipVertical=true\n- step 5: patternId=square, rotation=0, flipVertical=true\n- allowed patternId values for this task: O, K, square, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C125"} +{"sample_id": "C126", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> S -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "S", "E", "E"], "observed_path_faces": [{"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C126_path_sequence.png"}, "metadata": {"level_id": 126, "name": "Reconstruct 126", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-126.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["D", "D", "R", "arrow_down", "diamond", "2"], "start_x": 2, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "D", "rotation": 180}, "BOTTOM": {"patternId": "2", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 180}, "BACK": {"patternId": "arrow_down", "rotation": 0}, "LEFT": {"patternId": "diamond", "rotation": 180}, "RIGHT": {"patternId": "R", "rotation": 270}}, "bottom_faces": [{"patternId": "2", "rotation": 0, "x": 2, "y": 1}, {"patternId": "diamond", "rotation": 90, "x": 1, "y": 1}, {"patternId": "D", "rotation": 90, "x": 1, "y": 2}, {"patternId": "R", "rotation": 180, "x": 1, "y": 3}, {"patternId": "2", "rotation": 180, "x": 2, "y": 3}, {"patternId": "diamond", "rotation": 270, "x": 3, "y": 3}], "slot_sequence": ["LEFT", "FRONT", "RIGHT", "BOTTOM", "LEFT"], "required_slots": ["LEFT", "FRONT", "RIGHT", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "2", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "diamond", "rotation": 270}, "RIGHT": {"patternId": "R", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "2", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "diamond", "rotation": 270}, "RIGHT": {"patternId": "R", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C126\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> S -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=diamond, rotation=90, flipVertical=true\n- step 2: patternId=D, rotation=90, flipVertical=true\n- step 3: patternId=R, rotation=180, flipVertical=true\n- step 4: patternId=2, rotation=180, flipVertical=true\n- step 5: patternId=diamond, rotation=270, flipVertical=true\n- allowed patternId values for this task: diamond, D, R, 2, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C126"} +{"sample_id": "C127", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "S", "W"], "observed_path_faces": [{"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C127_path_sequence.png"}, "metadata": {"level_id": 127, "name": "Reconstruct 127", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-127.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["9", "Q", "6", "7", "X", "J"], "start_x": 2, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "9", "rotation": 270}, "BOTTOM": {"patternId": "J", "rotation": 180}, "FRONT": {"patternId": "Q", "rotation": 0}, "BACK": {"patternId": "7", "rotation": 0}, "LEFT": {"patternId": "X", "rotation": 270}, "RIGHT": {"patternId": "6", "rotation": 180}}, "bottom_faces": [{"patternId": "J", "rotation": 180, "x": 2, "y": 3}, {"patternId": "7", "rotation": 180, "x": 2, "y": 2}, {"patternId": "9", "rotation": 270, "x": 2, "y": 1}, {"patternId": "7", "rotation": 180, "x": 2, "y": 2}, {"patternId": "X", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["BACK", "TOP", "BACK", "LEFT"], "required_slots": ["BACK", "TOP", "LEFT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "9", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "X", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "9", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "X", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C127\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=7, rotation=180, flipVertical=true\n- step 2: patternId=9, rotation=270, flipVertical=true\n- step 3: patternId=7, rotation=180, flipVertical=true\n- step 4: patternId=X, rotation=90, flipVertical=true\n- allowed patternId values for this task: 7, 9, X, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C127"} +{"sample_id": "C128", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "E", "S"], "observed_path_faces": [{"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C128_path_sequence.png"}, "metadata": {"level_id": 128, "name": "Reconstruct 128", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-128.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["square", "circle", "N", "C", "circle", "M"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "square", "rotation": 180}, "BOTTOM": {"patternId": "M", "rotation": 270}, "FRONT": {"patternId": "circle", "rotation": 270}, "BACK": {"patternId": "C", "rotation": 90}, "LEFT": {"patternId": "circle", "rotation": 180}, "RIGHT": {"patternId": "N", "rotation": 90}}, "bottom_faces": [{"patternId": "M", "rotation": 270, "x": 1, "y": 1}, {"patternId": "N", "rotation": 180, "x": 2, "y": 1}, {"patternId": "circle", "rotation": 0, "x": 2, "y": 2}, {"patternId": "square", "rotation": 270, "x": 3, "y": 2}, {"patternId": "circle", "rotation": 0, "x": 3, "y": 3}], "slot_sequence": ["RIGHT", "FRONT", "TOP", "LEFT"], "required_slots": ["RIGHT", "FRONT", "TOP", "LEFT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "square", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "circle", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 270}, "RIGHT": {"patternId": "N", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "square", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "circle", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 270}, "RIGHT": {"patternId": "N", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C128\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=N, rotation=180, flipVertical=true\n- step 2: patternId=circle, rotation=0, flipVertical=true\n- step 3: patternId=square, rotation=270, flipVertical=true\n- step 4: patternId=circle, rotation=0, flipVertical=true\n- allowed patternId values for this task: N, circle, square, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C128"} +{"sample_id": "C129", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "W", "N"], "observed_path_faces": [{"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C129_path_sequence.png"}, "metadata": {"level_id": 129, "name": "Reconstruct 129", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-129.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["K", "X", "D", "T", "J", "F"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "K", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 180}, "FRONT": {"patternId": "X", "rotation": 180}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "J", "rotation": 180}, "RIGHT": {"patternId": "D", "rotation": 180}}, "bottom_faces": [{"patternId": "F", "rotation": 180, "x": 1, "y": 1}, {"patternId": "D", "rotation": 270, "x": 2, "y": 1}, {"patternId": "X", "rotation": 270, "x": 2, "y": 2}, {"patternId": "F", "rotation": 270, "x": 1, "y": 2}, {"patternId": "D", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["RIGHT", "FRONT", "BOTTOM", "RIGHT"], "required_slots": ["RIGHT", "FRONT", "BOTTOM"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 180}, "FRONT": {"patternId": "X", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 180}, "FRONT": {"patternId": "X", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C129\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=D, rotation=270, flipVertical=true\n- step 2: patternId=X, rotation=270, flipVertical=true\n- step 3: patternId=F, rotation=270, flipVertical=true\n- step 4: patternId=D, rotation=0, flipVertical=true\n- allowed patternId values for this task: D, X, F, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C129"} +{"sample_id": "C130", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> W -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "W", "S", "W"], "observed_path_faces": [{"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C130_path_sequence.png"}, "metadata": {"level_id": 130, "name": "Reconstruct 130", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-130.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["M", "arrow_right", "diamond", "V", "Z", "plus"], "start_x": 3, "start_y": 3, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "M", "rotation": 180}, "BOTTOM": {"patternId": "plus", "rotation": 180}, "FRONT": {"patternId": "arrow_right", "rotation": 180}, "BACK": {"patternId": "V", "rotation": 270}, "LEFT": {"patternId": "Z", "rotation": 180}, "RIGHT": {"patternId": "diamond", "rotation": 0}}, "bottom_faces": [{"patternId": "plus", "rotation": 180, "x": 3, "y": 3}, {"patternId": "V", "rotation": 90, "x": 3, "y": 2}, {"patternId": "M", "rotation": 180, "x": 3, "y": 1}, {"patternId": "Z", "rotation": 270, "x": 2, "y": 1}, {"patternId": "V", "rotation": 0, "x": 2, "y": 2}, {"patternId": "plus", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["BACK", "TOP", "LEFT", "BACK", "BOTTOM"], "required_slots": ["BACK", "TOP", "LEFT", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "M", "rotation": 180}, "BOTTOM": {"patternId": "plus", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "V", "rotation": 90}, "LEFT": {"patternId": "Z", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 180}, "BOTTOM": {"patternId": "plus", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "V", "rotation": 90}, "LEFT": {"patternId": "Z", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C130\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> W -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=V, rotation=90, flipVertical=true\n- step 2: patternId=M, rotation=180, flipVertical=true\n- step 3: patternId=Z, rotation=270, flipVertical=true\n- step 4: patternId=V, rotation=0, flipVertical=true\n- step 5: patternId=plus, rotation=90, flipVertical=true\n- allowed patternId values for this task: V, M, Z, plus, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C130"} +{"sample_id": "C131", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "S", "S"], "observed_path_faces": [{"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C131_path_sequence.png"}, "metadata": {"level_id": 131, "name": "Reconstruct 131", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-131.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_left", "E", "G", "F", "J", "I"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "arrow_left", "rotation": 90}, "BOTTOM": {"patternId": "I", "rotation": 0}, "FRONT": {"patternId": "E", "rotation": 90}, "BACK": {"patternId": "F", "rotation": 90}, "LEFT": {"patternId": "J", "rotation": 90}, "RIGHT": {"patternId": "G", "rotation": 90}}, "bottom_faces": [{"patternId": "I", "rotation": 0, "x": 3, "y": 1}, {"patternId": "J", "rotation": 0, "x": 2, "y": 1}, {"patternId": "arrow_left", "rotation": 270, "x": 1, "y": 1}, {"patternId": "E", "rotation": 270, "x": 1, "y": 2}, {"patternId": "I", "rotation": 180, "x": 1, "y": 3}], "slot_sequence": ["LEFT", "TOP", "FRONT", "BOTTOM"], "required_slots": ["LEFT", "TOP", "FRONT", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "arrow_left", "rotation": 90}, "BOTTOM": {"patternId": "I", "rotation": 0}, "FRONT": {"patternId": "E", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "J", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "arrow_left", "rotation": 90}, "BOTTOM": {"patternId": "I", "rotation": 0}, "FRONT": {"patternId": "E", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "J", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C131\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=J, rotation=0, flipVertical=true\n- step 2: patternId=arrow_left, rotation=270, flipVertical=true\n- step 3: patternId=E, rotation=270, flipVertical=true\n- step 4: patternId=I, rotation=180, flipVertical=true\n- allowed patternId values for this task: J, arrow_left, E, I, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C131"} +{"sample_id": "C132", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> N -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "N", "N", "N"], "observed_path_faces": [{"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C132_path_sequence.png"}, "metadata": {"level_id": 132, "name": "Reconstruct 132", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-132.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["W", "I", "triangle", "H", "S", "smile"], "start_x": 1, "start_y": 3, "grid_width": 3, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "W", "rotation": 180}, "BOTTOM": {"patternId": "smile", "rotation": 270}, "FRONT": {"patternId": "I", "rotation": 180}, "BACK": {"patternId": "H", "rotation": 180}, "LEFT": {"patternId": "S", "rotation": 0}, "RIGHT": {"patternId": "triangle", "rotation": 180}}, "bottom_faces": [{"patternId": "smile", "rotation": 270, "x": 1, "y": 3}, {"patternId": "I", "rotation": 180, "x": 1, "y": 4}, {"patternId": "smile", "rotation": 270, "x": 1, "y": 3}, {"patternId": "H", "rotation": 0, "x": 1, "y": 2}, {"patternId": "W", "rotation": 180, "x": 1, "y": 1}], "slot_sequence": ["FRONT", "BOTTOM", "BACK", "TOP"], "required_slots": ["FRONT", "BOTTOM", "BACK", "TOP"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "W", "rotation": 180}, "BOTTOM": {"patternId": "smile", "rotation": 270}, "FRONT": {"patternId": "I", "rotation": 180}, "BACK": {"patternId": "H", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "W", "rotation": 180}, "BOTTOM": {"patternId": "smile", "rotation": 270}, "FRONT": {"patternId": "I", "rotation": 180}, "BACK": {"patternId": "H", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C132\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): S -> N -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=I, rotation=180, flipVertical=true\n- step 2: patternId=smile, rotation=270, flipVertical=true\n- step 3: patternId=H, rotation=0, flipVertical=true\n- step 4: patternId=W, rotation=180, flipVertical=true\n- allowed patternId values for this task: I, smile, H, W, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C132"} +{"sample_id": "C133", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "S", "W"], "observed_path_faces": [{"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C133_path_sequence.png"}, "metadata": {"level_id": 133, "name": "Reconstruct 133", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-133.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["F", "square", "W", "heart", "arrow_right", "N"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "F", "rotation": 90}, "BOTTOM": {"patternId": "N", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 0}, "LEFT": {"patternId": "arrow_right", "rotation": 90}, "RIGHT": {"patternId": "W", "rotation": 270}}, "bottom_faces": [{"patternId": "N", "rotation": 0, "x": 2, "y": 1}, {"patternId": "square", "rotation": 0, "x": 2, "y": 2}, {"patternId": "F", "rotation": 90, "x": 2, "y": 3}, {"patternId": "heart", "rotation": 180, "x": 2, "y": 4}, {"patternId": "arrow_right", "rotation": 270, "x": 1, "y": 4}], "slot_sequence": ["FRONT", "TOP", "BACK", "LEFT"], "required_slots": ["FRONT", "TOP", "BACK", "LEFT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "F", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 180}, "LEFT": {"patternId": "arrow_right", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "F", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 180}, "LEFT": {"patternId": "arrow_right", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C133\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=square, rotation=0, flipVertical=true\n- step 2: patternId=F, rotation=90, flipVertical=true\n- step 3: patternId=heart, rotation=180, flipVertical=true\n- step 4: patternId=arrow_right, rotation=270, flipVertical=true\n- allowed patternId values for this task: square, F, heart, arrow_right, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C133"} +{"sample_id": "C134", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> N -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "N", "S", "E"], "observed_path_faces": [{"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C134_path_sequence.png"}, "metadata": {"level_id": 134, "name": "Reconstruct 134", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-134.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["star", "H", "Q", "5", "circle", "smile"], "start_x": 1, "start_y": 4, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "star", "rotation": 270}, "BOTTOM": {"patternId": "smile", "rotation": 90}, "FRONT": {"patternId": "H", "rotation": 90}, "BACK": {"patternId": "5", "rotation": 180}, "LEFT": {"patternId": "circle", "rotation": 90}, "RIGHT": {"patternId": "Q", "rotation": 180}}, "bottom_faces": [{"patternId": "smile", "rotation": 90, "x": 1, "y": 4}, {"patternId": "5", "rotation": 0, "x": 1, "y": 3}, {"patternId": "star", "rotation": 270, "x": 1, "y": 2}, {"patternId": "H", "rotation": 90, "x": 1, "y": 1}, {"patternId": "star", "rotation": 270, "x": 1, "y": 2}, {"patternId": "Q", "rotation": 90, "x": 2, "y": 2}], "slot_sequence": ["BACK", "TOP", "FRONT", "TOP", "RIGHT"], "required_slots": ["BACK", "TOP", "FRONT", "RIGHT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "star", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 90}, "BACK": {"patternId": "5", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Q", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 90}, "BACK": {"patternId": "5", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Q", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C134\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> N -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=5, rotation=0, flipVertical=true\n- step 2: patternId=star, rotation=270, flipVertical=true\n- step 3: patternId=H, rotation=90, flipVertical=true\n- step 4: patternId=star, rotation=270, flipVertical=true\n- step 5: patternId=Q, rotation=90, flipVertical=true\n- allowed patternId values for this task: 5, star, H, Q, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C134"} +{"sample_id": "C135", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "W", "W"], "observed_path_faces": [{"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C135_path_sequence.png"}, "metadata": {"level_id": 135, "name": "Reconstruct 135", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-135.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["E", "9", "arrow_down", "T", "V", "arrow_up"], "start_x": 2, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "E", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 0}, "FRONT": {"patternId": "9", "rotation": 270}, "BACK": {"patternId": "T", "rotation": 0}, "LEFT": {"patternId": "V", "rotation": 180}, "RIGHT": {"patternId": "arrow_down", "rotation": 180}}, "bottom_faces": [{"patternId": "arrow_up", "rotation": 0, "x": 2, "y": 1}, {"patternId": "arrow_down", "rotation": 270, "x": 3, "y": 1}, {"patternId": "9", "rotation": 0, "x": 3, "y": 2}, {"patternId": "arrow_up", "rotation": 90, "x": 2, "y": 2}, {"patternId": "T", "rotation": 270, "x": 1, "y": 2}], "slot_sequence": ["RIGHT", "FRONT", "BOTTOM", "BACK"], "required_slots": ["RIGHT", "FRONT", "BOTTOM", "BACK"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 0}, "FRONT": {"patternId": "9", "rotation": 270}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_down", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 0}, "FRONT": {"patternId": "9", "rotation": 270}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_down", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C135\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_down, rotation=270, flipVertical=true\n- step 2: patternId=9, rotation=0, flipVertical=true\n- step 3: patternId=arrow_up, rotation=90, flipVertical=true\n- step 4: patternId=T, rotation=270, flipVertical=true\n- allowed patternId values for this task: arrow_down, 9, arrow_up, T, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C135"} +{"sample_id": "C136", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> N -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "N", "W", "W"], "observed_path_faces": [{"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C136_path_sequence.png"}, "metadata": {"level_id": 136, "name": "Reconstruct 136", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-136.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["2", "S", "C", "2", "arrow_up", "diamond"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "2", "rotation": 90}, "BOTTOM": {"patternId": "diamond", "rotation": 90}, "FRONT": {"patternId": "S", "rotation": 180}, "BACK": {"patternId": "2", "rotation": 270}, "LEFT": {"patternId": "arrow_up", "rotation": 0}, "RIGHT": {"patternId": "C", "rotation": 270}}, "bottom_faces": [{"patternId": "diamond", "rotation": 90, "x": 3, "y": 1}, {"patternId": "S", "rotation": 180, "x": 3, "y": 2}, {"patternId": "diamond", "rotation": 90, "x": 3, "y": 1}, {"patternId": "arrow_up", "rotation": 270, "x": 2, "y": 1}, {"patternId": "2", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["FRONT", "BOTTOM", "LEFT", "TOP"], "required_slots": ["FRONT", "BOTTOM", "LEFT", "TOP"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "2", "rotation": 90}, "BOTTOM": {"patternId": "diamond", "rotation": 90}, "FRONT": {"patternId": "S", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_up", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "2", "rotation": 90}, "BOTTOM": {"patternId": "diamond", "rotation": 90}, "FRONT": {"patternId": "S", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_up", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C136\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): S -> N -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=S, rotation=180, flipVertical=true\n- step 2: patternId=diamond, rotation=90, flipVertical=true\n- step 3: patternId=arrow_up, rotation=270, flipVertical=true\n- step 4: patternId=2, rotation=270, flipVertical=true\n- allowed patternId values for this task: S, diamond, arrow_up, 2, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C136"} +{"sample_id": "C137", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "S", "N"], "observed_path_faces": [{"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C137_path_sequence.png"}, "metadata": {"level_id": 137, "name": "Reconstruct 137", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-137.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_left", "B", "7", "plus", "G", "P"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "arrow_left", "rotation": 0}, "BOTTOM": {"patternId": "P", "rotation": 90}, "FRONT": {"patternId": "B", "rotation": 90}, "BACK": {"patternId": "plus", "rotation": 0}, "LEFT": {"patternId": "G", "rotation": 180}, "RIGHT": {"patternId": "7", "rotation": 270}}, "bottom_faces": [{"patternId": "P", "rotation": 90, "x": 1, "y": 1}, {"patternId": "7", "rotation": 0, "x": 2, "y": 1}, {"patternId": "arrow_left", "rotation": 180, "x": 3, "y": 1}, {"patternId": "B", "rotation": 270, "x": 3, "y": 2}, {"patternId": "arrow_left", "rotation": 180, "x": 3, "y": 1}], "slot_sequence": ["RIGHT", "TOP", "FRONT", "TOP"], "required_slots": ["RIGHT", "TOP", "FRONT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "arrow_left", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "7", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "arrow_left", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "7", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C137\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=7, rotation=0, flipVertical=true\n- step 2: patternId=arrow_left, rotation=180, flipVertical=true\n- step 3: patternId=B, rotation=270, flipVertical=true\n- step 4: patternId=arrow_left, rotation=180, flipVertical=true\n- allowed patternId values for this task: 7, arrow_left, B, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C137"} +{"sample_id": "C138", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "W", "W"], "observed_path_faces": [{"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C138_path_sequence.png"}, "metadata": {"level_id": 138, "name": "Reconstruct 138", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-138.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["G", "Z", "5", "circle", "4", "2"], "start_x": 2, "start_y": 2, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "G", "rotation": 270}, "BOTTOM": {"patternId": "2", "rotation": 90}, "FRONT": {"patternId": "Z", "rotation": 90}, "BACK": {"patternId": "circle", "rotation": 0}, "LEFT": {"patternId": "4", "rotation": 270}, "RIGHT": {"patternId": "5", "rotation": 180}}, "bottom_faces": [{"patternId": "2", "rotation": 90, "x": 2, "y": 2}, {"patternId": "circle", "rotation": 180, "x": 2, "y": 1}, {"patternId": "5", "rotation": 0, "x": 3, "y": 1}, {"patternId": "circle", "rotation": 180, "x": 2, "y": 1}, {"patternId": "4", "rotation": 90, "x": 1, "y": 1}], "slot_sequence": ["BACK", "RIGHT", "BACK", "LEFT"], "required_slots": ["BACK", "RIGHT", "LEFT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 180}, "LEFT": {"patternId": "4", "rotation": 0}, "RIGHT": {"patternId": "5", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 180}, "LEFT": {"patternId": "4", "rotation": 0}, "RIGHT": {"patternId": "5", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C138\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=circle, rotation=180, flipVertical=true\n- step 2: patternId=5, rotation=0, flipVertical=true\n- step 3: patternId=circle, rotation=180, flipVertical=true\n- step 4: patternId=4, rotation=90, flipVertical=true\n- allowed patternId values for this task: circle, 5, 4, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C138"} +{"sample_id": "C139", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> N -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "N", "E", "E"], "observed_path_faces": [{"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C139_path_sequence.png"}, "metadata": {"level_id": 139, "name": "Reconstruct 139", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-139.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["S", "smile", "H", "V", "A", "A"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "S", "rotation": 90}, "BOTTOM": {"patternId": "A", "rotation": 0}, "FRONT": {"patternId": "smile", "rotation": 180}, "BACK": {"patternId": "V", "rotation": 270}, "LEFT": {"patternId": "A", "rotation": 90}, "RIGHT": {"patternId": "H", "rotation": 180}}, "bottom_faces": [{"patternId": "A", "rotation": 0, "x": 1, "y": 1}, {"patternId": "smile", "rotation": 180, "x": 1, "y": 2}, {"patternId": "A", "rotation": 0, "x": 1, "y": 1}, {"patternId": "H", "rotation": 270, "x": 2, "y": 1}, {"patternId": "S", "rotation": 270, "x": 3, "y": 1}], "slot_sequence": ["FRONT", "BOTTOM", "RIGHT", "TOP"], "required_slots": ["FRONT", "BOTTOM", "RIGHT", "TOP"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "S", "rotation": 90}, "BOTTOM": {"patternId": "A", "rotation": 0}, "FRONT": {"patternId": "smile", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "H", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 90}, "BOTTOM": {"patternId": "A", "rotation": 0}, "FRONT": {"patternId": "smile", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "H", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C139\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): S -> N -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=smile, rotation=180, flipVertical=true\n- step 2: patternId=A, rotation=0, flipVertical=true\n- step 3: patternId=H, rotation=270, flipVertical=true\n- step 4: patternId=S, rotation=270, flipVertical=true\n- allowed patternId values for this task: smile, A, H, S, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C139"} +{"sample_id": "C140", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> W -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "W", "S", "S"], "observed_path_faces": [{"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C140_path_sequence.png"}, "metadata": {"level_id": 140, "name": "Reconstruct 140", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-140.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["U", "G", "M", "S", "U", "N"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "U", "rotation": 90}, "BOTTOM": {"patternId": "N", "rotation": 0}, "FRONT": {"patternId": "G", "rotation": 90}, "BACK": {"patternId": "S", "rotation": 270}, "LEFT": {"patternId": "U", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 90}}, "bottom_faces": [{"patternId": "N", "rotation": 0, "x": 1, "y": 1}, {"patternId": "M", "rotation": 180, "x": 2, "y": 1}, {"patternId": "N", "rotation": 0, "x": 1, "y": 1}, {"patternId": "G", "rotation": 90, "x": 1, "y": 2}, {"patternId": "U", "rotation": 90, "x": 1, "y": 3}], "slot_sequence": ["RIGHT", "BOTTOM", "FRONT", "TOP"], "required_slots": ["RIGHT", "BOTTOM", "FRONT", "TOP"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "U", "rotation": 90}, "BOTTOM": {"patternId": "N", "rotation": 0}, "FRONT": {"patternId": "G", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "U", "rotation": 90}, "BOTTOM": {"patternId": "N", "rotation": 0}, "FRONT": {"patternId": "G", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C140\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> W -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=M, rotation=180, flipVertical=true\n- step 2: patternId=N, rotation=0, flipVertical=true\n- step 3: patternId=G, rotation=90, flipVertical=true\n- step 4: patternId=U, rotation=90, flipVertical=true\n- allowed patternId values for this task: M, N, G, U, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C140"} +{"sample_id": "C141", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "S", "E"], "observed_path_faces": [{"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C141_path_sequence.png"}, "metadata": {"level_id": 141, "name": "Reconstruct 141", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-141.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["O", "arrow_left", "6", "D", "W", "C"], "start_x": 1, "start_y": 2, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "O", "rotation": 0}, "BOTTOM": {"patternId": "C", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 180}, "BACK": {"patternId": "D", "rotation": 180}, "LEFT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "6", "rotation": 0}}, "bottom_faces": [{"patternId": "C", "rotation": 0, "x": 1, "y": 2}, {"patternId": "D", "rotation": 0, "x": 1, "y": 1}, {"patternId": "6", "rotation": 180, "x": 2, "y": 1}, {"patternId": "C", "rotation": 90, "x": 2, "y": 2}, {"patternId": "arrow_left", "rotation": 270, "x": 3, "y": 2}], "slot_sequence": ["BACK", "RIGHT", "BOTTOM", "FRONT"], "required_slots": ["BACK", "RIGHT", "BOTTOM", "FRONT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "C", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 180}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "C", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 180}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C141\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=D, rotation=0, flipVertical=true\n- step 2: patternId=6, rotation=180, flipVertical=true\n- step 3: patternId=C, rotation=90, flipVertical=true\n- step 4: patternId=arrow_left, rotation=270, flipVertical=true\n- allowed patternId values for this task: D, 6, C, arrow_left, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C141"} +{"sample_id": "C142", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> W -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "W", "E", "E"], "observed_path_faces": [{"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C142_path_sequence.png"}, "metadata": {"level_id": 142, "name": "Reconstruct 142", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-142.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["V", "4", "W", "I", "arrow_down", "X"], "start_x": 3, "start_y": 2, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "V", "rotation": 0}, "BOTTOM": {"patternId": "X", "rotation": 270}, "FRONT": {"patternId": "4", "rotation": 180}, "BACK": {"patternId": "I", "rotation": 90}, "LEFT": {"patternId": "arrow_down", "rotation": 270}, "RIGHT": {"patternId": "W", "rotation": 270}}, "bottom_faces": [{"patternId": "X", "rotation": 270, "x": 3, "y": 2}, {"patternId": "arrow_down", "rotation": 180, "x": 2, "y": 2}, {"patternId": "I", "rotation": 0, "x": 2, "y": 1}, {"patternId": "V", "rotation": 90, "x": 1, "y": 1}, {"patternId": "I", "rotation": 0, "x": 2, "y": 1}, {"patternId": "X", "rotation": 0, "x": 3, "y": 1}], "slot_sequence": ["LEFT", "BACK", "TOP", "BACK", "BOTTOM"], "required_slots": ["LEFT", "BACK", "TOP", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "V", "rotation": 0}, "BOTTOM": {"patternId": "X", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "arrow_down", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "V", "rotation": 0}, "BOTTOM": {"patternId": "X", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "arrow_down", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C142\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> W -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_down, rotation=180, flipVertical=true\n- step 2: patternId=I, rotation=0, flipVertical=true\n- step 3: patternId=V, rotation=90, flipVertical=true\n- step 4: patternId=I, rotation=0, flipVertical=true\n- step 5: patternId=X, rotation=0, flipVertical=true\n- allowed patternId values for this task: arrow_down, I, V, X, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C142"} +{"sample_id": "C143", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "W", "N"], "observed_path_faces": [{"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C143_path_sequence.png"}, "metadata": {"level_id": 143, "name": "Reconstruct 143", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-143.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["star", "M", "L", "J", "4", "K"], "start_x": 1, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "star", "rotation": 180}, "BOTTOM": {"patternId": "K", "rotation": 180}, "FRONT": {"patternId": "M", "rotation": 90}, "BACK": {"patternId": "J", "rotation": 270}, "LEFT": {"patternId": "4", "rotation": 0}, "RIGHT": {"patternId": "L", "rotation": 270}}, "bottom_faces": [{"patternId": "K", "rotation": 180, "x": 1, "y": 3}, {"patternId": "J", "rotation": 90, "x": 1, "y": 2}, {"patternId": "L", "rotation": 90, "x": 2, "y": 2}, {"patternId": "J", "rotation": 90, "x": 1, "y": 2}, {"patternId": "star", "rotation": 180, "x": 1, "y": 1}], "slot_sequence": ["BACK", "RIGHT", "BACK", "TOP"], "required_slots": ["BACK", "RIGHT", "TOP"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "star", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "J", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "L", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "J", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "L", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C143\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=J, rotation=90, flipVertical=true\n- step 2: patternId=L, rotation=90, flipVertical=true\n- step 3: patternId=J, rotation=90, flipVertical=true\n- step 4: patternId=star, rotation=180, flipVertical=true\n- allowed patternId values for this task: J, L, star, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C143"} +{"sample_id": "C144", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> N -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "N", "N", "W"], "observed_path_faces": [{"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C144_path_sequence.png"}, "metadata": {"level_id": 144, "name": "Reconstruct 144", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-144.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["L", "I", "K", "L", "8", "9"], "start_x": 3, "start_y": 4, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "L", "rotation": 90}, "BOTTOM": {"patternId": "9", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 270}, "BACK": {"patternId": "L", "rotation": 270}, "LEFT": {"patternId": "8", "rotation": 270}, "RIGHT": {"patternId": "K", "rotation": 270}}, "bottom_faces": [{"patternId": "9", "rotation": 0, "x": 3, "y": 4}, {"patternId": "L", "rotation": 90, "x": 3, "y": 3}, {"patternId": "8", "rotation": 90, "x": 2, "y": 3}, {"patternId": "L", "rotation": 180, "x": 2, "y": 2}, {"patternId": "K", "rotation": 270, "x": 2, "y": 1}, {"patternId": "I", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["BACK", "LEFT", "TOP", "RIGHT", "FRONT"], "required_slots": ["BACK", "LEFT", "TOP", "RIGHT", "FRONT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "L", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 270}, "BACK": {"patternId": "L", "rotation": 90}, "LEFT": {"patternId": "8", "rotation": 0}, "RIGHT": {"patternId": "K", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "L", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 270}, "BACK": {"patternId": "L", "rotation": 90}, "LEFT": {"patternId": "8", "rotation": 0}, "RIGHT": {"patternId": "K", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C144\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> N -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=L, rotation=90, flipVertical=true\n- step 2: patternId=8, rotation=90, flipVertical=true\n- step 3: patternId=L, rotation=180, flipVertical=true\n- step 4: patternId=K, rotation=270, flipVertical=true\n- step 5: patternId=I, rotation=270, flipVertical=true\n- allowed patternId values for this task: L, 8, K, I, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C144"} +{"sample_id": "C145", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> E -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "E", "W", "S"], "observed_path_faces": [{"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C145_path_sequence.png"}, "metadata": {"level_id": 145, "name": "Reconstruct 145", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-145.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["X", "U", "K", "A", "D", "Z"], "start_x": 1, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "X", "rotation": 270}, "BOTTOM": {"patternId": "Z", "rotation": 180}, "FRONT": {"patternId": "U", "rotation": 270}, "BACK": {"patternId": "A", "rotation": 270}, "LEFT": {"patternId": "D", "rotation": 180}, "RIGHT": {"patternId": "K", "rotation": 180}}, "bottom_faces": [{"patternId": "Z", "rotation": 180, "x": 1, "y": 3}, {"patternId": "A", "rotation": 90, "x": 1, "y": 2}, {"patternId": "X", "rotation": 270, "x": 1, "y": 1}, {"patternId": "K", "rotation": 90, "x": 2, "y": 1}, {"patternId": "X", "rotation": 270, "x": 1, "y": 1}, {"patternId": "A", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["BACK", "TOP", "RIGHT", "TOP", "BACK"], "required_slots": ["BACK", "TOP", "RIGHT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "X", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "A", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "K", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "X", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "A", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "K", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C145\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> E -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=A, rotation=90, flipVertical=true\n- step 2: patternId=X, rotation=270, flipVertical=true\n- step 3: patternId=K, rotation=90, flipVertical=true\n- step 4: patternId=X, rotation=270, flipVertical=true\n- step 5: patternId=A, rotation=90, flipVertical=true\n- allowed patternId values for this task: A, X, K, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C145"} +{"sample_id": "C146", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> W -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "W", "W", "W"], "observed_path_faces": [{"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C146_path_sequence.png"}, "metadata": {"level_id": 146, "name": "Reconstruct 146", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-146.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["V", "Y", "H", "L", "2", "B"], "start_x": 3, "start_y": 2, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "V", "rotation": 270}, "BOTTOM": {"patternId": "B", "rotation": 90}, "FRONT": {"patternId": "Y", "rotation": 0}, "BACK": {"patternId": "L", "rotation": 180}, "LEFT": {"patternId": "2", "rotation": 180}, "RIGHT": {"patternId": "H", "rotation": 0}}, "bottom_faces": [{"patternId": "B", "rotation": 90, "x": 3, "y": 2}, {"patternId": "H", "rotation": 90, "x": 4, "y": 2}, {"patternId": "L", "rotation": 270, "x": 4, "y": 1}, {"patternId": "B", "rotation": 0, "x": 3, "y": 1}, {"patternId": "Y", "rotation": 270, "x": 2, "y": 1}, {"patternId": "V", "rotation": 180, "x": 1, "y": 1}], "slot_sequence": ["RIGHT", "BACK", "BOTTOM", "FRONT", "TOP"], "required_slots": ["RIGHT", "BACK", "BOTTOM", "FRONT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "V", "rotation": 270}, "BOTTOM": {"patternId": "B", "rotation": 90}, "FRONT": {"patternId": "Y", "rotation": 0}, "BACK": {"patternId": "L", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "H", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "V", "rotation": 270}, "BOTTOM": {"patternId": "B", "rotation": 90}, "FRONT": {"patternId": "Y", "rotation": 0}, "BACK": {"patternId": "L", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "H", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C146\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> W -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=H, rotation=90, flipVertical=true\n- step 2: patternId=L, rotation=270, flipVertical=true\n- step 3: patternId=B, rotation=0, flipVertical=true\n- step 4: patternId=Y, rotation=270, flipVertical=true\n- step 5: patternId=V, rotation=180, flipVertical=true\n- allowed patternId values for this task: H, L, B, Y, V, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C146"} +{"sample_id": "C147", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> E -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "E", "W", "W"], "observed_path_faces": [{"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C147_path_sequence.png"}, "metadata": {"level_id": 147, "name": "Reconstruct 147", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-147.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_down", "T", "R", "W", "M", "J"], "start_x": 1, "start_y": 2, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "arrow_down", "rotation": 180}, "BOTTOM": {"patternId": "J", "rotation": 0}, "FRONT": {"patternId": "T", "rotation": 0}, "BACK": {"patternId": "W", "rotation": 270}, "LEFT": {"patternId": "M", "rotation": 90}, "RIGHT": {"patternId": "R", "rotation": 270}}, "bottom_faces": [{"patternId": "J", "rotation": 0, "x": 1, "y": 2}, {"patternId": "W", "rotation": 90, "x": 1, "y": 1}, {"patternId": "R", "rotation": 90, "x": 2, "y": 1}, {"patternId": "T", "rotation": 180, "x": 3, "y": 1}, {"patternId": "R", "rotation": 90, "x": 2, "y": 1}, {"patternId": "W", "rotation": 90, "x": 1, "y": 1}], "slot_sequence": ["BACK", "RIGHT", "FRONT", "RIGHT", "BACK"], "required_slots": ["BACK", "RIGHT", "FRONT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "T", "rotation": 0}, "BACK": {"patternId": "W", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "T", "rotation": 0}, "BACK": {"patternId": "W", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C147\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> E -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=W, rotation=90, flipVertical=true\n- step 2: patternId=R, rotation=90, flipVertical=true\n- step 3: patternId=T, rotation=180, flipVertical=true\n- step 4: patternId=R, rotation=90, flipVertical=true\n- step 5: patternId=W, rotation=90, flipVertical=true\n- allowed patternId values for this task: W, R, T, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C147"} +{"sample_id": "C148", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> N -> N -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "N", "N", "S"], "observed_path_faces": [{"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C148_path_sequence.png"}, "metadata": {"level_id": 148, "name": "Reconstruct 148", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-148.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["star", "8", "5", "M", "2", "7"], "start_x": 3, "start_y": 3, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "star", "rotation": 0}, "BOTTOM": {"patternId": "7", "rotation": 270}, "FRONT": {"patternId": "8", "rotation": 90}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "2", "rotation": 90}, "RIGHT": {"patternId": "5", "rotation": 180}}, "bottom_faces": [{"patternId": "7", "rotation": 270, "x": 3, "y": 3}, {"patternId": "2", "rotation": 0, "x": 2, "y": 3}, {"patternId": "star", "rotation": 180, "x": 1, "y": 3}, {"patternId": "M", "rotation": 0, "x": 1, "y": 2}, {"patternId": "7", "rotation": 90, "x": 1, "y": 1}, {"patternId": "M", "rotation": 0, "x": 1, "y": 2}], "slot_sequence": ["LEFT", "TOP", "BACK", "BOTTOM", "BACK"], "required_slots": ["LEFT", "TOP", "BACK", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "star", "rotation": 0}, "BOTTOM": {"patternId": "7", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 180}, "LEFT": {"patternId": "2", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 0}, "BOTTOM": {"patternId": "7", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 180}, "LEFT": {"patternId": "2", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C148\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> N -> N -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=2, rotation=0, flipVertical=true\n- step 2: patternId=star, rotation=180, flipVertical=true\n- step 3: patternId=M, rotation=0, flipVertical=true\n- step 4: patternId=7, rotation=90, flipVertical=true\n- step 5: patternId=M, rotation=0, flipVertical=true\n- allowed patternId values for this task: 2, star, M, 7, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C148"} +{"sample_id": "C149", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> S -> S -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "S", "S", "W", "S"], "observed_path_faces": [{"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C149_path_sequence.png"}, "metadata": {"level_id": 149, "name": "Reconstruct 149", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-149.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["triangle", "R", "X", "star", "diamond", "B"], "start_x": 2, "start_y": 2, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "triangle", "rotation": 180}, "BOTTOM": {"patternId": "B", "rotation": 90}, "FRONT": {"patternId": "R", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 270}, "LEFT": {"patternId": "diamond", "rotation": 90}, "RIGHT": {"patternId": "X", "rotation": 0}}, "bottom_faces": [{"patternId": "B", "rotation": 90, "x": 2, "y": 2}, {"patternId": "star", "rotation": 90, "x": 2, "y": 1}, {"patternId": "B", "rotation": 90, "x": 2, "y": 2}, {"patternId": "R", "rotation": 0, "x": 2, "y": 3}, {"patternId": "diamond", "rotation": 90, "x": 1, "y": 3}, {"patternId": "triangle", "rotation": 90, "x": 1, "y": 4}], "slot_sequence": ["BACK", "BOTTOM", "FRONT", "LEFT", "TOP"], "required_slots": ["BACK", "BOTTOM", "FRONT", "LEFT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "triangle", "rotation": 180}, "BOTTOM": {"patternId": "B", "rotation": 90}, "FRONT": {"patternId": "R", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 90}, "LEFT": {"patternId": "diamond", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "triangle", "rotation": 180}, "BOTTOM": {"patternId": "B", "rotation": 90}, "FRONT": {"patternId": "R", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 90}, "LEFT": {"patternId": "diamond", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C149\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): N -> S -> S -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=star, rotation=90, flipVertical=true\n- step 2: patternId=B, rotation=90, flipVertical=true\n- step 3: patternId=R, rotation=0, flipVertical=true\n- step 4: patternId=diamond, rotation=90, flipVertical=true\n- step 5: patternId=triangle, rotation=90, flipVertical=true\n- allowed patternId values for this task: star, B, R, diamond, triangle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C149"} +{"sample_id": "C150", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> W -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "W", "W", "W"], "observed_path_faces": [{"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C150_path_sequence.png"}, "metadata": {"level_id": 150, "name": "Reconstruct 150", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-150.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["I", "N", "D", "2", "P", "Y"], "start_x": 5, "start_y": 2, "grid_width": 7, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "I", "rotation": 0}, "BOTTOM": {"patternId": "Y", "rotation": 270}, "FRONT": {"patternId": "N", "rotation": 180}, "BACK": {"patternId": "2", "rotation": 90}, "LEFT": {"patternId": "P", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 180}}, "bottom_faces": [{"patternId": "Y", "rotation": 270, "x": 5, "y": 2}, {"patternId": "P", "rotation": 270, "x": 4, "y": 2}, {"patternId": "2", "rotation": 0, "x": 4, "y": 1}, {"patternId": "I", "rotation": 90, "x": 3, "y": 1}, {"patternId": "N", "rotation": 270, "x": 2, "y": 1}, {"patternId": "Y", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "BACK", "TOP", "FRONT", "BOTTOM"], "required_slots": ["LEFT", "BACK", "TOP", "FRONT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "I", "rotation": 0}, "BOTTOM": {"patternId": "Y", "rotation": 270}, "FRONT": {"patternId": "N", "rotation": 180}, "BACK": {"patternId": "2", "rotation": 270}, "LEFT": {"patternId": "P", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 0}, "BOTTOM": {"patternId": "Y", "rotation": 270}, "FRONT": {"patternId": "N", "rotation": 180}, "BACK": {"patternId": "2", "rotation": 270}, "LEFT": {"patternId": "P", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C150\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> W -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=P, rotation=270, flipVertical=true\n- step 2: patternId=2, rotation=0, flipVertical=true\n- step 3: patternId=I, rotation=90, flipVertical=true\n- step 4: patternId=N, rotation=270, flipVertical=true\n- step 5: patternId=Y, rotation=0, flipVertical=true\n- allowed patternId values for this task: P, 2, I, N, Y, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C150"} +{"sample_id": "C151", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "E", "N"], "observed_path_faces": [{"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C151_path_sequence.png"}, "metadata": {"level_id": 151, "name": "Reconstruct 151", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-151.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Y", "F", "circle", "star", "arrow_up", "2"], "start_x": 2, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "Y", "rotation": 180}, "BOTTOM": {"patternId": "2", "rotation": 180}, "FRONT": {"patternId": "F", "rotation": 180}, "BACK": {"patternId": "star", "rotation": 90}, "LEFT": {"patternId": "arrow_up", "rotation": 180}, "RIGHT": {"patternId": "circle", "rotation": 90}}, "bottom_faces": [{"patternId": "2", "rotation": 180, "x": 2, "y": 3}, {"patternId": "star", "rotation": 270, "x": 2, "y": 2}, {"patternId": "arrow_up", "rotation": 0, "x": 1, "y": 2}, {"patternId": "star", "rotation": 270, "x": 2, "y": 2}, {"patternId": "Y", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["BACK", "LEFT", "BACK", "TOP"], "required_slots": ["BACK", "LEFT", "TOP"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "Y", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 270}, "LEFT": {"patternId": "arrow_up", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "Y", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 270}, "LEFT": {"patternId": "arrow_up", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C151\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=star, rotation=270, flipVertical=true\n- step 2: patternId=arrow_up, rotation=0, flipVertical=true\n- step 3: patternId=star, rotation=270, flipVertical=true\n- step 4: patternId=Y, rotation=180, flipVertical=true\n- allowed patternId values for this task: star, arrow_up, Y, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C151"} +{"sample_id": "C152", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> E -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "E", "W", "N"], "observed_path_faces": [{"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C152_path_sequence.png"}, "metadata": {"level_id": 152, "name": "Reconstruct 152", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-152.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["1", "heart", "O", "plus", "U", "6"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "1", "rotation": 180}, "BOTTOM": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "plus", "rotation": 0}, "LEFT": {"patternId": "U", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 0}}, "bottom_faces": [{"patternId": "6", "rotation": 180, "x": 2, "y": 1}, {"patternId": "U", "rotation": 270, "x": 1, "y": 1}, {"patternId": "heart", "rotation": 180, "x": 1, "y": 2}, {"patternId": "6", "rotation": 90, "x": 2, "y": 2}, {"patternId": "heart", "rotation": 180, "x": 1, "y": 2}, {"patternId": "U", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "FRONT", "BOTTOM", "FRONT", "LEFT"], "required_slots": ["LEFT", "FRONT", "BOTTOM"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "U", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "U", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C152\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> E -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=U, rotation=270, flipVertical=true\n- step 2: patternId=heart, rotation=180, flipVertical=true\n- step 3: patternId=6, rotation=90, flipVertical=true\n- step 4: patternId=heart, rotation=180, flipVertical=true\n- step 5: patternId=U, rotation=270, flipVertical=true\n- allowed patternId values for this task: U, heart, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C152"} +{"sample_id": "C153", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "E", "S"], "observed_path_faces": [{"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C153_path_sequence.png"}, "metadata": {"level_id": 153, "name": "Reconstruct 153", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-153.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["P", "2", "V", "C", "diamond", "7"], "start_x": 1, "start_y": 2, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "P", "rotation": 180}, "BOTTOM": {"patternId": "7", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 0}, "BACK": {"patternId": "C", "rotation": 180}, "LEFT": {"patternId": "diamond", "rotation": 90}, "RIGHT": {"patternId": "V", "rotation": 180}}, "bottom_faces": [{"patternId": "7", "rotation": 0, "x": 1, "y": 2}, {"patternId": "V", "rotation": 270, "x": 2, "y": 2}, {"patternId": "C", "rotation": 270, "x": 2, "y": 1}, {"patternId": "P", "rotation": 90, "x": 3, "y": 1}, {"patternId": "V", "rotation": 0, "x": 3, "y": 2}], "slot_sequence": ["RIGHT", "BACK", "TOP", "RIGHT"], "required_slots": ["RIGHT", "BACK", "TOP"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "P", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "C", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "V", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "P", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "C", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "V", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C153\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=V, rotation=270, flipVertical=true\n- step 2: patternId=C, rotation=270, flipVertical=true\n- step 3: patternId=P, rotation=90, flipVertical=true\n- step 4: patternId=V, rotation=0, flipVertical=true\n- allowed patternId values for this task: V, C, P, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C153"} +{"sample_id": "C154", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> W -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "W", "E"], "observed_path_faces": [{"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C154_path_sequence.png"}, "metadata": {"level_id": 154, "name": "Reconstruct 154", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-154.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["V", "7", "V", "G", "K", "R"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "V", "rotation": 0}, "BOTTOM": {"patternId": "R", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 0}, "BACK": {"patternId": "G", "rotation": 270}, "LEFT": {"patternId": "K", "rotation": 270}, "RIGHT": {"patternId": "V", "rotation": 270}}, "bottom_faces": [{"patternId": "R", "rotation": 0, "x": 3, "y": 1}, {"patternId": "K", "rotation": 180, "x": 2, "y": 1}, {"patternId": "7", "rotation": 270, "x": 2, "y": 2}, {"patternId": "V", "rotation": 270, "x": 1, "y": 2}, {"patternId": "7", "rotation": 270, "x": 2, "y": 2}], "slot_sequence": ["LEFT", "FRONT", "TOP", "FRONT"], "required_slots": ["LEFT", "FRONT", "TOP"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "V", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "K", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "V", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "K", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C154\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> W -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=K, rotation=180, flipVertical=true\n- step 2: patternId=7, rotation=270, flipVertical=true\n- step 3: patternId=V, rotation=270, flipVertical=true\n- step 4: patternId=7, rotation=270, flipVertical=true\n- allowed patternId values for this task: K, 7, V, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C154"} +{"sample_id": "C155", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> N -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "N", "E", "E"], "observed_path_faces": [{"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C155_path_sequence.png"}, "metadata": {"level_id": 155, "name": "Reconstruct 155", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-155.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["A", "1", "Y", "Y", "X", "K"], "start_x": 1, "start_y": 3, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "A", "rotation": 270}, "BOTTOM": {"patternId": "K", "rotation": 0}, "FRONT": {"patternId": "1", "rotation": 270}, "BACK": {"patternId": "Y", "rotation": 270}, "LEFT": {"patternId": "X", "rotation": 0}, "RIGHT": {"patternId": "Y", "rotation": 180}}, "bottom_faces": [{"patternId": "K", "rotation": 0, "x": 1, "y": 3}, {"patternId": "Y", "rotation": 270, "x": 2, "y": 3}, {"patternId": "Y", "rotation": 0, "x": 2, "y": 2}, {"patternId": "X", "rotation": 90, "x": 2, "y": 1}, {"patternId": "A", "rotation": 270, "x": 3, "y": 1}, {"patternId": "Y", "rotation": 90, "x": 4, "y": 1}], "slot_sequence": ["RIGHT", "BACK", "LEFT", "TOP", "RIGHT"], "required_slots": ["RIGHT", "BACK", "LEFT", "TOP"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "A", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "Y", "rotation": 90}, "LEFT": {"patternId": "X", "rotation": 90}, "RIGHT": {"patternId": "Y", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "A", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "Y", "rotation": 90}, "LEFT": {"patternId": "X", "rotation": 90}, "RIGHT": {"patternId": "Y", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C155\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> N -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Y, rotation=270, flipVertical=true\n- step 2: patternId=Y, rotation=0, flipVertical=true\n- step 3: patternId=X, rotation=90, flipVertical=true\n- step 4: patternId=A, rotation=270, flipVertical=true\n- step 5: patternId=Y, rotation=90, flipVertical=true\n- allowed patternId values for this task: Y, X, A, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C155"} +{"sample_id": "C156", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "E", "N"], "observed_path_faces": [{"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C156_path_sequence.png"}, "metadata": {"level_id": 156, "name": "Reconstruct 156", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-156.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["8", "F", "Q", "C", "heart", "1"], "start_x": 1, "start_y": 3, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "8", "rotation": 180}, "BOTTOM": {"patternId": "1", "rotation": 0}, "FRONT": {"patternId": "F", "rotation": 180}, "BACK": {"patternId": "C", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 90}, "RIGHT": {"patternId": "Q", "rotation": 180}}, "bottom_faces": [{"patternId": "1", "rotation": 0, "x": 1, "y": 3}, {"patternId": "Q", "rotation": 270, "x": 2, "y": 3}, {"patternId": "C", "rotation": 90, "x": 2, "y": 2}, {"patternId": "8", "rotation": 90, "x": 3, "y": 2}, {"patternId": "heart", "rotation": 90, "x": 3, "y": 1}], "slot_sequence": ["RIGHT", "BACK", "TOP", "LEFT"], "required_slots": ["RIGHT", "BACK", "TOP", "LEFT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "8", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "C", "rotation": 180}, "LEFT": {"patternId": "heart", "rotation": 180}, "RIGHT": {"patternId": "Q", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "8", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "C", "rotation": 180}, "LEFT": {"patternId": "heart", "rotation": 180}, "RIGHT": {"patternId": "Q", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C156\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Q, rotation=270, flipVertical=true\n- step 2: patternId=C, rotation=90, flipVertical=true\n- step 3: patternId=8, rotation=90, flipVertical=true\n- step 4: patternId=heart, rotation=90, flipVertical=true\n- allowed patternId values for this task: Q, C, 8, heart, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C156"} +{"sample_id": "C157", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> W -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "W", "N", "N"], "observed_path_faces": [{"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C157_path_sequence.png"}, "metadata": {"level_id": 157, "name": "Reconstruct 157", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-157.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_down", "star", "R", "R", "T", "6"], "start_x": 1, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "arrow_down", "rotation": 270}, "BOTTOM": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "star", "rotation": 180}, "BACK": {"patternId": "R", "rotation": 180}, "LEFT": {"patternId": "T", "rotation": 180}, "RIGHT": {"patternId": "R", "rotation": 270}}, "bottom_faces": [{"patternId": "6", "rotation": 180, "x": 1, "y": 3}, {"patternId": "R", "rotation": 0, "x": 2, "y": 3}, {"patternId": "6", "rotation": 180, "x": 1, "y": 3}, {"patternId": "R", "rotation": 0, "x": 1, "y": 2}, {"patternId": "arrow_down", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["RIGHT", "BOTTOM", "BACK", "TOP"], "required_slots": ["RIGHT", "BOTTOM", "BACK", "TOP"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "arrow_down", "rotation": 270}, "BOTTOM": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "arrow_down", "rotation": 270}, "BOTTOM": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C157\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> W -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=R, rotation=0, flipVertical=true\n- step 2: patternId=6, rotation=180, flipVertical=true\n- step 3: patternId=R, rotation=0, flipVertical=true\n- step 4: patternId=arrow_down, rotation=270, flipVertical=true\n- allowed patternId values for this task: R, 6, arrow_down, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C157"} +{"sample_id": "C158", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "S", "W"], "observed_path_faces": [{"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C158_path_sequence.png"}, "metadata": {"level_id": 158, "name": "Reconstruct 158", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-158.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["5", "U", "8", "K", "9", "star"], "start_x": 2, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "5", "rotation": 270}, "BOTTOM": {"patternId": "star", "rotation": 0}, "FRONT": {"patternId": "U", "rotation": 180}, "BACK": {"patternId": "K", "rotation": 90}, "LEFT": {"patternId": "9", "rotation": 0}, "RIGHT": {"patternId": "8", "rotation": 180}}, "bottom_faces": [{"patternId": "star", "rotation": 0, "x": 2, "y": 3}, {"patternId": "K", "rotation": 270, "x": 2, "y": 2}, {"patternId": "5", "rotation": 270, "x": 2, "y": 1}, {"patternId": "K", "rotation": 270, "x": 2, "y": 2}, {"patternId": "9", "rotation": 180, "x": 1, "y": 2}], "slot_sequence": ["BACK", "TOP", "BACK", "LEFT"], "required_slots": ["BACK", "TOP", "LEFT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "5", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "9", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "5", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "9", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C158\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=K, rotation=270, flipVertical=true\n- step 2: patternId=5, rotation=270, flipVertical=true\n- step 3: patternId=K, rotation=270, flipVertical=true\n- step 4: patternId=9, rotation=180, flipVertical=true\n- allowed patternId values for this task: K, 5, 9, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C158"} +{"sample_id": "C159", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> N -> N -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "N", "N", "S"], "observed_path_faces": [{"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C159_path_sequence.png"}, "metadata": {"level_id": 159, "name": "Reconstruct 159", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-159.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["1", "7", "2", "circle", "star", "V"], "start_x": 2, "start_y": 4, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "1", "rotation": 270}, "BOTTOM": {"patternId": "V", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 180}, "LEFT": {"patternId": "star", "rotation": 90}, "RIGHT": {"patternId": "2", "rotation": 90}}, "bottom_faces": [{"patternId": "V", "rotation": 0, "x": 2, "y": 4}, {"patternId": "star", "rotation": 0, "x": 1, "y": 4}, {"patternId": "circle", "rotation": 90, "x": 1, "y": 3}, {"patternId": "2", "rotation": 0, "x": 1, "y": 2}, {"patternId": "7", "rotation": 270, "x": 1, "y": 1}, {"patternId": "2", "rotation": 0, "x": 1, "y": 2}], "slot_sequence": ["LEFT", "BACK", "RIGHT", "FRONT", "RIGHT"], "required_slots": ["LEFT", "BACK", "RIGHT", "FRONT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 180}, "RIGHT": {"patternId": "2", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 180}, "RIGHT": {"patternId": "2", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C159\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> N -> N -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=star, rotation=0, flipVertical=true\n- step 2: patternId=circle, rotation=90, flipVertical=true\n- step 3: patternId=2, rotation=0, flipVertical=true\n- step 4: patternId=7, rotation=270, flipVertical=true\n- step 5: patternId=2, rotation=0, flipVertical=true\n- allowed patternId values for this task: star, circle, 2, 7, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C159"} +{"sample_id": "C160", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> E -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "E", "E", "E"], "observed_path_faces": [{"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C160_path_sequence.png"}, "metadata": {"level_id": 160, "name": "Reconstruct 160", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-160.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["D", "V", "circle", "O", "Q", "O"], "start_x": 2, "start_y": 1, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "D", "rotation": 270}, "BOTTOM": {"patternId": "O", "rotation": 90}, "FRONT": {"patternId": "V", "rotation": 180}, "BACK": {"patternId": "O", "rotation": 180}, "LEFT": {"patternId": "Q", "rotation": 90}, "RIGHT": {"patternId": "circle", "rotation": 270}}, "bottom_faces": [{"patternId": "O", "rotation": 90, "x": 2, "y": 1}, {"patternId": "Q", "rotation": 0, "x": 1, "y": 1}, {"patternId": "V", "rotation": 90, "x": 1, "y": 2}, {"patternId": "O", "rotation": 0, "x": 2, "y": 2}, {"patternId": "O", "rotation": 270, "x": 3, "y": 2}, {"patternId": "D", "rotation": 180, "x": 4, "y": 2}], "slot_sequence": ["LEFT", "FRONT", "BOTTOM", "BACK", "TOP"], "required_slots": ["LEFT", "FRONT", "BOTTOM", "BACK", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "D", "rotation": 270}, "BOTTOM": {"patternId": "O", "rotation": 90}, "FRONT": {"patternId": "V", "rotation": 180}, "BACK": {"patternId": "O", "rotation": 0}, "LEFT": {"patternId": "Q", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "D", "rotation": 270}, "BOTTOM": {"patternId": "O", "rotation": 90}, "FRONT": {"patternId": "V", "rotation": 180}, "BACK": {"patternId": "O", "rotation": 0}, "LEFT": {"patternId": "Q", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C160\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> E -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Q, rotation=0, flipVertical=true\n- step 2: patternId=V, rotation=90, flipVertical=true\n- step 3: patternId=O, rotation=0, flipVertical=true\n- step 4: patternId=O, rotation=270, flipVertical=true\n- step 5: patternId=D, rotation=180, flipVertical=true\n- allowed patternId values for this task: Q, V, O, D, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C160"} +{"sample_id": "C161", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> W -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "W", "N", "E"], "observed_path_faces": [{"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C161_path_sequence.png"}, "metadata": {"level_id": 161, "name": "Reconstruct 161", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-161.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Y", "square", "3", "W", "N", "B"], "start_x": 1, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "Y", "rotation": 180}, "BOTTOM": {"patternId": "B", "rotation": 90}, "FRONT": {"patternId": "square", "rotation": 0}, "BACK": {"patternId": "W", "rotation": 0}, "LEFT": {"patternId": "N", "rotation": 0}, "RIGHT": {"patternId": "3", "rotation": 270}}, "bottom_faces": [{"patternId": "B", "rotation": 90, "x": 1, "y": 3}, {"patternId": "W", "rotation": 180, "x": 1, "y": 2}, {"patternId": "3", "rotation": 90, "x": 2, "y": 2}, {"patternId": "W", "rotation": 180, "x": 1, "y": 2}, {"patternId": "Y", "rotation": 180, "x": 1, "y": 1}, {"patternId": "3", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["BACK", "RIGHT", "BACK", "TOP", "RIGHT"], "required_slots": ["BACK", "RIGHT", "TOP"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "Y", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "W", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "3", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "Y", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "W", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "3", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C161\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> W -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=W, rotation=180, flipVertical=true\n- step 2: patternId=3, rotation=90, flipVertical=true\n- step 3: patternId=W, rotation=180, flipVertical=true\n- step 4: patternId=Y, rotation=180, flipVertical=true\n- step 5: patternId=3, rotation=180, flipVertical=true\n- allowed patternId values for this task: W, 3, Y, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C161"} +{"sample_id": "C162", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> S -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "S", "E", "S"], "observed_path_faces": [{"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C162_path_sequence.png"}, "metadata": {"level_id": 162, "name": "Reconstruct 162", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-162.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Y", "V", "arrow_left", "L", "arrow_left", "I"], "start_x": 1, "start_y": 1, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "Y", "rotation": 180}, "BOTTOM": {"patternId": "I", "rotation": 180}, "FRONT": {"patternId": "V", "rotation": 180}, "BACK": {"patternId": "L", "rotation": 90}, "LEFT": {"patternId": "arrow_left", "rotation": 180}, "RIGHT": {"patternId": "arrow_left", "rotation": 180}}, "bottom_faces": [{"patternId": "I", "rotation": 180, "x": 1, "y": 1}, {"patternId": "arrow_left", "rotation": 270, "x": 2, "y": 1}, {"patternId": "Y", "rotation": 0, "x": 3, "y": 1}, {"patternId": "V", "rotation": 0, "x": 3, "y": 2}, {"patternId": "arrow_left", "rotation": 0, "x": 4, "y": 2}, {"patternId": "I", "rotation": 90, "x": 4, "y": 3}], "slot_sequence": ["RIGHT", "TOP", "FRONT", "LEFT", "BOTTOM"], "required_slots": ["RIGHT", "TOP", "FRONT", "LEFT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "Y", "rotation": 180}, "BOTTOM": {"patternId": "I", "rotation": 180}, "FRONT": {"patternId": "V", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 270}, "RIGHT": {"patternId": "arrow_left", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "Y", "rotation": 180}, "BOTTOM": {"patternId": "I", "rotation": 180}, "FRONT": {"patternId": "V", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 270}, "RIGHT": {"patternId": "arrow_left", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C162\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> S -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_left, rotation=270, flipVertical=true\n- step 2: patternId=Y, rotation=0, flipVertical=true\n- step 3: patternId=V, rotation=0, flipVertical=true\n- step 4: patternId=arrow_left, rotation=0, flipVertical=true\n- step 5: patternId=I, rotation=90, flipVertical=true\n- allowed patternId values for this task: arrow_left, Y, V, I, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C162"} +{"sample_id": "C163", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "N", "N"], "observed_path_faces": [{"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C163_path_sequence.png"}, "metadata": {"level_id": 163, "name": "Reconstruct 163", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-163.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["smile", "W", "S", "diamond", "G", "6"], "start_x": 2, "start_y": 4, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "smile", "rotation": 180}, "BOTTOM": {"patternId": "6", "rotation": 270}, "FRONT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "diamond", "rotation": 270}, "LEFT": {"patternId": "G", "rotation": 270}, "RIGHT": {"patternId": "S", "rotation": 90}}, "bottom_faces": [{"patternId": "6", "rotation": 270, "x": 2, "y": 4}, {"patternId": "diamond", "rotation": 90, "x": 2, "y": 3}, {"patternId": "G", "rotation": 90, "x": 1, "y": 3}, {"patternId": "smile", "rotation": 270, "x": 1, "y": 2}, {"patternId": "S", "rotation": 90, "x": 1, "y": 1}], "slot_sequence": ["BACK", "LEFT", "TOP", "RIGHT"], "required_slots": ["BACK", "LEFT", "TOP", "RIGHT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "smile", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "diamond", "rotation": 90}, "LEFT": {"patternId": "G", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "diamond", "rotation": 90}, "LEFT": {"patternId": "G", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C163\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=diamond, rotation=90, flipVertical=true\n- step 2: patternId=G, rotation=90, flipVertical=true\n- step 3: patternId=smile, rotation=270, flipVertical=true\n- step 4: patternId=S, rotation=90, flipVertical=true\n- allowed patternId values for this task: diamond, G, smile, S, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C163"} +{"sample_id": "C164", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> W -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "W", "E"], "observed_path_faces": [{"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C164_path_sequence.png"}, "metadata": {"level_id": 164, "name": "Reconstruct 164", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-164.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["P", "Q", "square", "J", "D", "L"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "P", "rotation": 270}, "BOTTOM": {"patternId": "L", "rotation": 0}, "FRONT": {"patternId": "Q", "rotation": 90}, "BACK": {"patternId": "J", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 180}, "RIGHT": {"patternId": "square", "rotation": 90}}, "bottom_faces": [{"patternId": "L", "rotation": 0, "x": 3, "y": 1}, {"patternId": "D", "rotation": 90, "x": 2, "y": 1}, {"patternId": "Q", "rotation": 0, "x": 2, "y": 2}, {"patternId": "P", "rotation": 180, "x": 1, "y": 2}, {"patternId": "Q", "rotation": 0, "x": 2, "y": 2}], "slot_sequence": ["LEFT", "FRONT", "TOP", "FRONT"], "required_slots": ["LEFT", "FRONT", "TOP"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "P", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "Q", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "P", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "Q", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C164\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> W -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=D, rotation=90, flipVertical=true\n- step 2: patternId=Q, rotation=0, flipVertical=true\n- step 3: patternId=P, rotation=180, flipVertical=true\n- step 4: patternId=Q, rotation=0, flipVertical=true\n- allowed patternId values for this task: D, Q, P, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C164"} +{"sample_id": "C165", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "W", "S"], "observed_path_faces": [{"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C165_path_sequence.png"}, "metadata": {"level_id": 165, "name": "Reconstruct 165", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-165.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["4", "2", "M", "6", "A", "star"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "4", "rotation": 270}, "BOTTOM": {"patternId": "star", "rotation": 180}, "FRONT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "6", "rotation": 270}, "LEFT": {"patternId": "A", "rotation": 180}, "RIGHT": {"patternId": "M", "rotation": 90}}, "bottom_faces": [{"patternId": "star", "rotation": 180, "x": 1, "y": 1}, {"patternId": "M", "rotation": 180, "x": 2, "y": 1}, {"patternId": "2", "rotation": 0, "x": 2, "y": 2}, {"patternId": "star", "rotation": 270, "x": 1, "y": 2}, {"patternId": "A", "rotation": 180, "x": 1, "y": 3}], "slot_sequence": ["RIGHT", "FRONT", "BOTTOM", "LEFT"], "required_slots": ["RIGHT", "FRONT", "BOTTOM", "LEFT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "star", "rotation": 180}, "FRONT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "A", "rotation": 270}, "RIGHT": {"patternId": "M", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "star", "rotation": 180}, "FRONT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "A", "rotation": 270}, "RIGHT": {"patternId": "M", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C165\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=M, rotation=180, flipVertical=true\n- step 2: patternId=2, rotation=0, flipVertical=true\n- step 3: patternId=star, rotation=270, flipVertical=true\n- step 4: patternId=A, rotation=180, flipVertical=true\n- allowed patternId values for this task: M, 2, star, A, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C165"} +{"sample_id": "C166", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "W", "S", "S"], "observed_path_faces": [{"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C166_path_sequence.png"}, "metadata": {"level_id": 166, "name": "Reconstruct 166", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-166.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["circle", "diamond", "smile", "plus", "arrow_up", "Q"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "circle", "rotation": 270}, "BOTTOM": {"patternId": "Q", "rotation": 180}, "FRONT": {"patternId": "diamond", "rotation": 0}, "BACK": {"patternId": "plus", "rotation": 90}, "LEFT": {"patternId": "arrow_up", "rotation": 0}, "RIGHT": {"patternId": "smile", "rotation": 180}}, "bottom_faces": [{"patternId": "Q", "rotation": 180, "x": 1, "y": 1}, {"patternId": "smile", "rotation": 270, "x": 2, "y": 1}, {"patternId": "diamond", "rotation": 90, "x": 2, "y": 2}, {"patternId": "Q", "rotation": 270, "x": 1, "y": 2}, {"patternId": "arrow_up", "rotation": 0, "x": 1, "y": 3}, {"patternId": "circle", "rotation": 180, "x": 1, "y": 4}], "slot_sequence": ["RIGHT", "FRONT", "BOTTOM", "LEFT", "TOP"], "required_slots": ["RIGHT", "FRONT", "BOTTOM", "LEFT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "circle", "rotation": 270}, "BOTTOM": {"patternId": "Q", "rotation": 180}, "FRONT": {"patternId": "diamond", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_up", "rotation": 90}, "RIGHT": {"patternId": "smile", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 270}, "BOTTOM": {"patternId": "Q", "rotation": 180}, "FRONT": {"patternId": "diamond", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_up", "rotation": 90}, "RIGHT": {"patternId": "smile", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C166\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=smile, rotation=270, flipVertical=true\n- step 2: patternId=diamond, rotation=90, flipVertical=true\n- step 3: patternId=Q, rotation=270, flipVertical=true\n- step 4: patternId=arrow_up, rotation=0, flipVertical=true\n- step 5: patternId=circle, rotation=180, flipVertical=true\n- allowed patternId values for this task: smile, diamond, Q, arrow_up, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C166"} +{"sample_id": "C167", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "W", "S"], "observed_path_faces": [{"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C167_path_sequence.png"}, "metadata": {"level_id": 167, "name": "Reconstruct 167", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-167.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["O", "8", "plus", "B", "S", "arrow_down"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "O", "rotation": 90}, "BOTTOM": {"patternId": "arrow_down", "rotation": 180}, "FRONT": {"patternId": "8", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 180}, "LEFT": {"patternId": "S", "rotation": 270}, "RIGHT": {"patternId": "plus", "rotation": 0}}, "bottom_faces": [{"patternId": "arrow_down", "rotation": 180, "x": 2, "y": 1}, {"patternId": "8", "rotation": 0, "x": 2, "y": 2}, {"patternId": "O", "rotation": 90, "x": 2, "y": 3}, {"patternId": "S", "rotation": 0, "x": 1, "y": 3}, {"patternId": "B", "rotation": 270, "x": 1, "y": 4}], "slot_sequence": ["FRONT", "TOP", "LEFT", "BACK"], "required_slots": ["FRONT", "TOP", "LEFT", "BACK"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "O", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "8", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "S", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "8", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "S", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C167\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=8, rotation=0, flipVertical=true\n- step 2: patternId=O, rotation=90, flipVertical=true\n- step 3: patternId=S, rotation=0, flipVertical=true\n- step 4: patternId=B, rotation=270, flipVertical=true\n- allowed patternId values for this task: 8, O, S, B, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C167"} +{"sample_id": "C168", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "E", "S"], "observed_path_faces": [{"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C168_path_sequence.png"}, "metadata": {"level_id": 168, "name": "Reconstruct 168", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-168.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["7", "V", "V", "square", "8", "Q"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "7", "rotation": 0}, "BOTTOM": {"patternId": "Q", "rotation": 0}, "FRONT": {"patternId": "V", "rotation": 90}, "BACK": {"patternId": "square", "rotation": 180}, "LEFT": {"patternId": "8", "rotation": 270}, "RIGHT": {"patternId": "V", "rotation": 90}}, "bottom_faces": [{"patternId": "Q", "rotation": 0, "x": 3, "y": 1}, {"patternId": "8", "rotation": 180, "x": 2, "y": 1}, {"patternId": "7", "rotation": 180, "x": 1, "y": 1}, {"patternId": "8", "rotation": 180, "x": 2, "y": 1}, {"patternId": "V", "rotation": 0, "x": 2, "y": 2}], "slot_sequence": ["LEFT", "TOP", "LEFT", "FRONT"], "required_slots": ["LEFT", "TOP", "FRONT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "7", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "V", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "7", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "V", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C168\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=8, rotation=180, flipVertical=true\n- step 2: patternId=7, rotation=180, flipVertical=true\n- step 3: patternId=8, rotation=180, flipVertical=true\n- step 4: patternId=V, rotation=0, flipVertical=true\n- allowed patternId values for this task: 8, 7, V, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C168"} +{"sample_id": "C169", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "W", "S"], "observed_path_faces": [{"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C169_path_sequence.png"}, "metadata": {"level_id": 169, "name": "Reconstruct 169", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-169.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["D", "Q", "4", "U", "M", "M"], "start_x": 4, "start_y": 1, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "D", "rotation": 90}, "BOTTOM": {"patternId": "M", "rotation": 270}, "FRONT": {"patternId": "Q", "rotation": 180}, "BACK": {"patternId": "U", "rotation": 90}, "LEFT": {"patternId": "M", "rotation": 90}, "RIGHT": {"patternId": "4", "rotation": 90}}, "bottom_faces": [{"patternId": "M", "rotation": 270, "x": 4, "y": 1}, {"patternId": "M", "rotation": 0, "x": 3, "y": 1}, {"patternId": "D", "rotation": 270, "x": 2, "y": 1}, {"patternId": "4", "rotation": 180, "x": 1, "y": 1}, {"patternId": "Q", "rotation": 270, "x": 1, "y": 2}], "slot_sequence": ["LEFT", "TOP", "RIGHT", "FRONT"], "required_slots": ["LEFT", "TOP", "RIGHT", "FRONT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "D", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "Q", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "M", "rotation": 180}, "RIGHT": {"patternId": "4", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "D", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "Q", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "M", "rotation": 180}, "RIGHT": {"patternId": "4", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C169\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=M, rotation=0, flipVertical=true\n- step 2: patternId=D, rotation=270, flipVertical=true\n- step 3: patternId=4, rotation=180, flipVertical=true\n- step 4: patternId=Q, rotation=270, flipVertical=true\n- allowed patternId values for this task: M, D, 4, Q, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C169"} +{"sample_id": "C170", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "S", "S"], "observed_path_faces": [{"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C170_path_sequence.png"}, "metadata": {"level_id": 170, "name": "Reconstruct 170", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-170.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["triangle", "6", "B", "G", "3", "4"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "triangle", "rotation": 180}, "BOTTOM": {"patternId": "4", "rotation": 180}, "FRONT": {"patternId": "6", "rotation": 0}, "BACK": {"patternId": "G", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 0}, "RIGHT": {"patternId": "B", "rotation": 90}}, "bottom_faces": [{"patternId": "4", "rotation": 180, "x": 1, "y": 2}, {"patternId": "G", "rotation": 180, "x": 1, "y": 1}, {"patternId": "B", "rotation": 270, "x": 2, "y": 1}, {"patternId": "4", "rotation": 270, "x": 2, "y": 2}, {"patternId": "3", "rotation": 0, "x": 2, "y": 3}], "slot_sequence": ["BACK", "RIGHT", "BOTTOM", "LEFT"], "required_slots": ["BACK", "RIGHT", "BOTTOM", "LEFT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "4", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "G", "rotation": 180}, "LEFT": {"patternId": "3", "rotation": 90}, "RIGHT": {"patternId": "B", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "4", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "G", "rotation": 180}, "LEFT": {"patternId": "3", "rotation": 90}, "RIGHT": {"patternId": "B", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C170\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=G, rotation=180, flipVertical=true\n- step 2: patternId=B, rotation=270, flipVertical=true\n- step 3: patternId=4, rotation=270, flipVertical=true\n- step 4: patternId=3, rotation=0, flipVertical=true\n- allowed patternId values for this task: G, B, 4, 3, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C170"} +{"sample_id": "C171", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> W -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "W", "E", "E"], "observed_path_faces": [{"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C171_path_sequence.png"}, "metadata": {"level_id": 171, "name": "Reconstruct 171", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-171.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["E", "H", "4", "5", "5", "E"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "E", "rotation": 90}, "BOTTOM": {"patternId": "E", "rotation": 270}, "FRONT": {"patternId": "H", "rotation": 270}, "BACK": {"patternId": "5", "rotation": 180}, "LEFT": {"patternId": "5", "rotation": 90}, "RIGHT": {"patternId": "4", "rotation": 90}}, "bottom_faces": [{"patternId": "E", "rotation": 270, "x": 3, "y": 1}, {"patternId": "5", "rotation": 0, "x": 2, "y": 1}, {"patternId": "H", "rotation": 180, "x": 2, "y": 2}, {"patternId": "E", "rotation": 0, "x": 1, "y": 2}, {"patternId": "H", "rotation": 180, "x": 2, "y": 2}, {"patternId": "E", "rotation": 180, "x": 3, "y": 2}], "slot_sequence": ["LEFT", "FRONT", "TOP", "FRONT", "BOTTOM"], "required_slots": ["LEFT", "FRONT", "TOP", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "E", "rotation": 90}, "BOTTOM": {"patternId": "E", "rotation": 270}, "FRONT": {"patternId": "H", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "5", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "E", "rotation": 90}, "BOTTOM": {"patternId": "E", "rotation": 270}, "FRONT": {"patternId": "H", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "5", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C171\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> W -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=5, rotation=0, flipVertical=true\n- step 2: patternId=H, rotation=180, flipVertical=true\n- step 3: patternId=E, rotation=0, flipVertical=true\n- step 4: patternId=H, rotation=180, flipVertical=true\n- step 5: patternId=E, rotation=180, flipVertical=true\n- allowed patternId values for this task: 5, H, E, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C171"} +{"sample_id": "C172", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> E -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "E", "E", "S"], "observed_path_faces": [{"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C172_path_sequence.png"}, "metadata": {"level_id": 172, "name": "Reconstruct 172", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-172.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["L", "6", "I", "K", "W", "M"], "start_x": 1, "start_y": 3, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "L", "rotation": 180}, "BOTTOM": {"patternId": "M", "rotation": 180}, "FRONT": {"patternId": "6", "rotation": 90}, "BACK": {"patternId": "K", "rotation": 180}, "LEFT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "I", "rotation": 0}}, "bottom_faces": [{"patternId": "M", "rotation": 180, "x": 1, "y": 3}, {"patternId": "K", "rotation": 0, "x": 1, "y": 2}, {"patternId": "L", "rotation": 180, "x": 1, "y": 1}, {"patternId": "I", "rotation": 270, "x": 2, "y": 1}, {"patternId": "M", "rotation": 0, "x": 3, "y": 1}, {"patternId": "K", "rotation": 180, "x": 3, "y": 2}], "slot_sequence": ["BACK", "TOP", "RIGHT", "BOTTOM", "BACK"], "required_slots": ["BACK", "TOP", "RIGHT", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "L", "rotation": 180}, "BOTTOM": {"patternId": "M", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "L", "rotation": 180}, "BOTTOM": {"patternId": "M", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C172\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> E -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=K, rotation=0, flipVertical=true\n- step 2: patternId=L, rotation=180, flipVertical=true\n- step 3: patternId=I, rotation=270, flipVertical=true\n- step 4: patternId=M, rotation=0, flipVertical=true\n- step 5: patternId=K, rotation=180, flipVertical=true\n- allowed patternId values for this task: K, L, I, M, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C172"} +{"sample_id": "C173", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "N", "E"], "observed_path_faces": [{"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C173_path_sequence.png"}, "metadata": {"level_id": 173, "name": "Reconstruct 173", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-173.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["I", "5", "J", "7", "E", "C"], "start_x": 1, "start_y": 2, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "I", "rotation": 90}, "BOTTOM": {"patternId": "C", "rotation": 0}, "FRONT": {"patternId": "5", "rotation": 0}, "BACK": {"patternId": "7", "rotation": 90}, "LEFT": {"patternId": "E", "rotation": 270}, "RIGHT": {"patternId": "J", "rotation": 180}}, "bottom_faces": [{"patternId": "C", "rotation": 0, "x": 1, "y": 2}, {"patternId": "J", "rotation": 270, "x": 2, "y": 2}, {"patternId": "I", "rotation": 270, "x": 3, "y": 2}, {"patternId": "7", "rotation": 90, "x": 3, "y": 1}, {"patternId": "E", "rotation": 270, "x": 4, "y": 1}], "slot_sequence": ["RIGHT", "TOP", "BACK", "LEFT"], "required_slots": ["RIGHT", "TOP", "BACK", "LEFT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "I", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "7", "rotation": 270}, "LEFT": {"patternId": "E", "rotation": 0}, "RIGHT": {"patternId": "J", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "7", "rotation": 270}, "LEFT": {"patternId": "E", "rotation": 0}, "RIGHT": {"patternId": "J", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C173\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=J, rotation=270, flipVertical=true\n- step 2: patternId=I, rotation=270, flipVertical=true\n- step 3: patternId=7, rotation=90, flipVertical=true\n- step 4: patternId=E, rotation=270, flipVertical=true\n- allowed patternId values for this task: J, I, 7, E, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C173"} +{"sample_id": "C174", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> N -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "N", "E", "E"], "observed_path_faces": [{"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C174_path_sequence.png"}, "metadata": {"level_id": 174, "name": "Reconstruct 174", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-174.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["P", "R", "E", "Z", "U", "X"], "start_x": 1, "start_y": 4, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "P", "rotation": 0}, "BOTTOM": {"patternId": "X", "rotation": 90}, "FRONT": {"patternId": "R", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 0}, "LEFT": {"patternId": "U", "rotation": 270}, "RIGHT": {"patternId": "E", "rotation": 180}}, "bottom_faces": [{"patternId": "X", "rotation": 90, "x": 1, "y": 4}, {"patternId": "Z", "rotation": 180, "x": 1, "y": 3}, {"patternId": "P", "rotation": 0, "x": 1, "y": 2}, {"patternId": "R", "rotation": 180, "x": 1, "y": 1}, {"patternId": "E", "rotation": 180, "x": 2, "y": 1}, {"patternId": "Z", "rotation": 0, "x": 3, "y": 1}], "slot_sequence": ["BACK", "TOP", "FRONT", "RIGHT", "BACK"], "required_slots": ["BACK", "TOP", "FRONT", "RIGHT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "P", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "R", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "E", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "P", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "R", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "E", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C174\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> N -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Z, rotation=180, flipVertical=true\n- step 2: patternId=P, rotation=0, flipVertical=true\n- step 3: patternId=R, rotation=180, flipVertical=true\n- step 4: patternId=E, rotation=180, flipVertical=true\n- step 5: patternId=Z, rotation=0, flipVertical=true\n- allowed patternId values for this task: Z, P, R, E, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C174"} +{"sample_id": "C175", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> W -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "W", "E", "N"], "observed_path_faces": [{"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C175_path_sequence.png"}, "metadata": {"level_id": 175, "name": "Reconstruct 175", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-175.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["8", "diamond", "arrow_down", "P", "5", "H"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "8", "rotation": 180}, "BOTTOM": {"patternId": "H", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 270}, "BACK": {"patternId": "P", "rotation": 90}, "LEFT": {"patternId": "5", "rotation": 0}, "RIGHT": {"patternId": "arrow_down", "rotation": 270}}, "bottom_faces": [{"patternId": "H", "rotation": 0, "x": 3, "y": 1}, {"patternId": "diamond", "rotation": 270, "x": 3, "y": 2}, {"patternId": "5", "rotation": 0, "x": 2, "y": 2}, {"patternId": "P", "rotation": 90, "x": 1, "y": 2}, {"patternId": "5", "rotation": 0, "x": 2, "y": 2}, {"patternId": "H", "rotation": 90, "x": 2, "y": 1}], "slot_sequence": ["FRONT", "LEFT", "BACK", "LEFT", "BOTTOM"], "required_slots": ["FRONT", "LEFT", "BACK", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "H", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 270}, "BACK": {"patternId": "P", "rotation": 270}, "LEFT": {"patternId": "5", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "H", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 270}, "BACK": {"patternId": "P", "rotation": 270}, "LEFT": {"patternId": "5", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C175\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> W -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=diamond, rotation=270, flipVertical=true\n- step 2: patternId=5, rotation=0, flipVertical=true\n- step 3: patternId=P, rotation=90, flipVertical=true\n- step 4: patternId=5, rotation=0, flipVertical=true\n- step 5: patternId=H, rotation=90, flipVertical=true\n- allowed patternId values for this task: diamond, 5, P, H, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C175"} +{"sample_id": "C176", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> E -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "E", "E", "N"], "observed_path_faces": [{"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C176_path_sequence.png"}, "metadata": {"level_id": 176, "name": "Reconstruct 176", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-176.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["M", "1", "A", "E", "F", "O"], "start_x": 2, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "M", "rotation": 0}, "BOTTOM": {"patternId": "O", "rotation": 90}, "FRONT": {"patternId": "1", "rotation": 0}, "BACK": {"patternId": "E", "rotation": 270}, "LEFT": {"patternId": "F", "rotation": 270}, "RIGHT": {"patternId": "A", "rotation": 270}}, "bottom_faces": [{"patternId": "O", "rotation": 90, "x": 2, "y": 1}, {"patternId": "F", "rotation": 180, "x": 1, "y": 1}, {"patternId": "1", "rotation": 270, "x": 1, "y": 2}, {"patternId": "O", "rotation": 0, "x": 2, "y": 2}, {"patternId": "E", "rotation": 0, "x": 3, "y": 2}, {"patternId": "F", "rotation": 0, "x": 3, "y": 1}], "slot_sequence": ["LEFT", "FRONT", "BOTTOM", "BACK", "LEFT"], "required_slots": ["LEFT", "FRONT", "BOTTOM", "BACK"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "O", "rotation": 90}, "FRONT": {"patternId": "1", "rotation": 0}, "BACK": {"patternId": "E", "rotation": 90}, "LEFT": {"patternId": "F", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "O", "rotation": 90}, "FRONT": {"patternId": "1", "rotation": 0}, "BACK": {"patternId": "E", "rotation": 90}, "LEFT": {"patternId": "F", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C176\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> E -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=F, rotation=180, flipVertical=true\n- step 2: patternId=1, rotation=270, flipVertical=true\n- step 3: patternId=O, rotation=0, flipVertical=true\n- step 4: patternId=E, rotation=0, flipVertical=true\n- step 5: patternId=F, rotation=0, flipVertical=true\n- allowed patternId values for this task: F, 1, O, E, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C176"} +{"sample_id": "C177", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> S -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "S", "E", "N"], "observed_path_faces": [{"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C177_path_sequence.png"}, "metadata": {"level_id": 177, "name": "Reconstruct 177", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-177.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Y", "S", "arrow_right", "star", "plus", "W"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "Y", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 0}, "FRONT": {"patternId": "S", "rotation": 180}, "BACK": {"patternId": "star", "rotation": 90}, "LEFT": {"patternId": "plus", "rotation": 90}, "RIGHT": {"patternId": "arrow_right", "rotation": 0}}, "bottom_faces": [{"patternId": "W", "rotation": 0, "x": 1, "y": 2}, {"patternId": "star", "rotation": 270, "x": 1, "y": 1}, {"patternId": "W", "rotation": 0, "x": 1, "y": 2}, {"patternId": "arrow_right", "rotation": 90, "x": 2, "y": 2}, {"patternId": "star", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["BACK", "BOTTOM", "RIGHT", "BACK"], "required_slots": ["BACK", "BOTTOM", "RIGHT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C177\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): N -> S -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=star, rotation=270, flipVertical=true\n- step 2: patternId=W, rotation=0, flipVertical=true\n- step 3: patternId=arrow_right, rotation=90, flipVertical=true\n- step 4: patternId=star, rotation=180, flipVertical=true\n- allowed patternId values for this task: star, W, arrow_right, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C177"} +{"sample_id": "C178", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "W", "W"], "observed_path_faces": [{"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C178_path_sequence.png"}, "metadata": {"level_id": 178, "name": "Reconstruct 178", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-178.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["P", "arrow_down", "D", "F", "J", "5"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "P", "rotation": 90}, "BOTTOM": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "arrow_down", "rotation": 180}, "BACK": {"patternId": "F", "rotation": 270}, "LEFT": {"patternId": "J", "rotation": 90}, "RIGHT": {"patternId": "D", "rotation": 180}}, "bottom_faces": [{"patternId": "5", "rotation": 90, "x": 3, "y": 1}, {"patternId": "arrow_down", "rotation": 180, "x": 3, "y": 2}, {"patternId": "P", "rotation": 90, "x": 3, "y": 3}, {"patternId": "J", "rotation": 180, "x": 2, "y": 3}, {"patternId": "5", "rotation": 270, "x": 1, "y": 3}], "slot_sequence": ["FRONT", "TOP", "LEFT", "BOTTOM"], "required_slots": ["FRONT", "TOP", "LEFT", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "P", "rotation": 90}, "BOTTOM": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "arrow_down", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "J", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "P", "rotation": 90}, "BOTTOM": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "arrow_down", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "J", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C178\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_down, rotation=180, flipVertical=true\n- step 2: patternId=P, rotation=90, flipVertical=true\n- step 3: patternId=J, rotation=180, flipVertical=true\n- step 4: patternId=5, rotation=270, flipVertical=true\n- allowed patternId values for this task: arrow_down, P, J, 5, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C178"} +{"sample_id": "C179", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> S -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "S", "S", "E"], "observed_path_faces": [{"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C179_path_sequence.png"}, "metadata": {"level_id": 179, "name": "Reconstruct 179", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-179.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["L", "N", "J", "E", "circle", "H"], "start_x": 1, "start_y": 1, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "L", "rotation": 0}, "BOTTOM": {"patternId": "H", "rotation": 270}, "FRONT": {"patternId": "N", "rotation": 270}, "BACK": {"patternId": "E", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 0}, "RIGHT": {"patternId": "J", "rotation": 180}}, "bottom_faces": [{"patternId": "H", "rotation": 270, "x": 1, "y": 1}, {"patternId": "J", "rotation": 270, "x": 2, "y": 1}, {"patternId": "L", "rotation": 180, "x": 3, "y": 1}, {"patternId": "N", "rotation": 90, "x": 3, "y": 2}, {"patternId": "H", "rotation": 90, "x": 3, "y": 3}, {"patternId": "circle", "rotation": 90, "x": 4, "y": 3}], "slot_sequence": ["RIGHT", "TOP", "FRONT", "BOTTOM", "LEFT"], "required_slots": ["RIGHT", "TOP", "FRONT", "BOTTOM", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "L", "rotation": 0}, "BOTTOM": {"patternId": "H", "rotation": 270}, "FRONT": {"patternId": "N", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 90}, "RIGHT": {"patternId": "J", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "L", "rotation": 0}, "BOTTOM": {"patternId": "H", "rotation": 270}, "FRONT": {"patternId": "N", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 90}, "RIGHT": {"patternId": "J", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C179\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> S -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=J, rotation=270, flipVertical=true\n- step 2: patternId=L, rotation=180, flipVertical=true\n- step 3: patternId=N, rotation=90, flipVertical=true\n- step 4: patternId=H, rotation=90, flipVertical=true\n- step 5: patternId=circle, rotation=90, flipVertical=true\n- allowed patternId values for this task: J, L, N, H, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C179"} +{"sample_id": "C180", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "W", "N"], "observed_path_faces": [{"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C180_path_sequence.png"}, "metadata": {"level_id": 180, "name": "Reconstruct 180", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-180.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_up", "7", "C", "triangle", "W", "X"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "arrow_up", "rotation": 180}, "BOTTOM": {"patternId": "X", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 270}, "BACK": {"patternId": "triangle", "rotation": 270}, "LEFT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "C", "rotation": 180}}, "bottom_faces": [{"patternId": "X", "rotation": 0, "x": 3, "y": 1}, {"patternId": "W", "rotation": 0, "x": 2, "y": 1}, {"patternId": "7", "rotation": 180, "x": 2, "y": 2}, {"patternId": "arrow_up", "rotation": 90, "x": 1, "y": 2}, {"patternId": "W", "rotation": 90, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "FRONT", "TOP", "LEFT"], "required_slots": ["LEFT", "FRONT", "TOP"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "arrow_up", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "arrow_up", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C180\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=W, rotation=0, flipVertical=true\n- step 2: patternId=7, rotation=180, flipVertical=true\n- step 3: patternId=arrow_up, rotation=90, flipVertical=true\n- step 4: patternId=W, rotation=90, flipVertical=true\n- allowed patternId values for this task: W, 7, arrow_up, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C180"} +{"sample_id": "C181", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> W -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "W", "W", "W"], "observed_path_faces": [{"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C181_path_sequence.png"}, "metadata": {"level_id": 181, "name": "Reconstruct 181", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-181.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["5", "J", "Z", "7", "diamond", "F"], "start_x": 3, "start_y": 1, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "5", "rotation": 180}, "BOTTOM": {"patternId": "F", "rotation": 180}, "FRONT": {"patternId": "J", "rotation": 0}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "diamond", "rotation": 180}, "RIGHT": {"patternId": "Z", "rotation": 180}}, "bottom_faces": [{"patternId": "F", "rotation": 180, "x": 3, "y": 1}, {"patternId": "J", "rotation": 0, "x": 3, "y": 2}, {"patternId": "Z", "rotation": 180, "x": 4, "y": 2}, {"patternId": "J", "rotation": 0, "x": 3, "y": 2}, {"patternId": "diamond", "rotation": 180, "x": 2, "y": 2}, {"patternId": "7", "rotation": 180, "x": 1, "y": 2}], "slot_sequence": ["FRONT", "RIGHT", "FRONT", "LEFT", "BACK"], "required_slots": ["FRONT", "RIGHT", "LEFT", "BACK"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 0}, "BACK": {"patternId": "7", "rotation": 0}, "LEFT": {"patternId": "diamond", "rotation": 270}, "RIGHT": {"patternId": "Z", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 0}, "BACK": {"patternId": "7", "rotation": 0}, "LEFT": {"patternId": "diamond", "rotation": 270}, "RIGHT": {"patternId": "Z", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C181\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> W -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=J, rotation=0, flipVertical=true\n- step 2: patternId=Z, rotation=180, flipVertical=true\n- step 3: patternId=J, rotation=0, flipVertical=true\n- step 4: patternId=diamond, rotation=180, flipVertical=true\n- step 5: patternId=7, rotation=180, flipVertical=true\n- allowed patternId values for this task: J, Z, diamond, 7, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C181"} +{"sample_id": "C182", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "S", "N"], "observed_path_faces": [{"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C182_path_sequence.png"}, "metadata": {"level_id": 182, "name": "Reconstruct 182", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-182.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["plus", "1", "4", "T", "V", "Z"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "plus", "rotation": 270}, "BOTTOM": {"patternId": "Z", "rotation": 0}, "FRONT": {"patternId": "1", "rotation": 180}, "BACK": {"patternId": "T", "rotation": 90}, "LEFT": {"patternId": "V", "rotation": 180}, "RIGHT": {"patternId": "4", "rotation": 180}}, "bottom_faces": [{"patternId": "Z", "rotation": 0, "x": 2, "y": 1}, {"patternId": "V", "rotation": 90, "x": 1, "y": 1}, {"patternId": "1", "rotation": 90, "x": 1, "y": 2}, {"patternId": "4", "rotation": 90, "x": 1, "y": 3}, {"patternId": "1", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["LEFT", "FRONT", "RIGHT", "FRONT"], "required_slots": ["LEFT", "FRONT", "RIGHT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "1", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "V", "rotation": 270}, "RIGHT": {"patternId": "4", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "1", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "V", "rotation": 270}, "RIGHT": {"patternId": "4", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C182\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=V, rotation=90, flipVertical=true\n- step 2: patternId=1, rotation=90, flipVertical=true\n- step 3: patternId=4, rotation=90, flipVertical=true\n- step 4: patternId=1, rotation=90, flipVertical=true\n- allowed patternId values for this task: V, 1, 4, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C182"} +{"sample_id": "C183", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> W -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "W", "W", "E"], "observed_path_faces": [{"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C183_path_sequence.png"}, "metadata": {"level_id": 183, "name": "Reconstruct 183", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-183.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["I", "G", "smile", "D", "W", "8"], "start_x": 2, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "I", "rotation": 180}, "BOTTOM": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "G", "rotation": 180}, "BACK": {"patternId": "D", "rotation": 270}, "LEFT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "smile", "rotation": 0}}, "bottom_faces": [{"patternId": "8", "rotation": 180, "x": 2, "y": 1}, {"patternId": "smile", "rotation": 90, "x": 3, "y": 1}, {"patternId": "G", "rotation": 270, "x": 3, "y": 2}, {"patternId": "8", "rotation": 270, "x": 2, "y": 2}, {"patternId": "D", "rotation": 180, "x": 1, "y": 2}, {"patternId": "8", "rotation": 270, "x": 2, "y": 2}], "slot_sequence": ["RIGHT", "FRONT", "BOTTOM", "BACK", "BOTTOM"], "required_slots": ["RIGHT", "FRONT", "BOTTOM", "BACK"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "G", "rotation": 180}, "BACK": {"patternId": "D", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "smile", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "G", "rotation": 180}, "BACK": {"patternId": "D", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "smile", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C183\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> W -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=smile, rotation=90, flipVertical=true\n- step 2: patternId=G, rotation=270, flipVertical=true\n- step 3: patternId=8, rotation=270, flipVertical=true\n- step 4: patternId=D, rotation=180, flipVertical=true\n- step 5: patternId=8, rotation=270, flipVertical=true\n- allowed patternId values for this task: smile, G, 8, D, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C183"} +{"sample_id": "C184", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "E", "N"], "observed_path_faces": [{"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C184_path_sequence.png"}, "metadata": {"level_id": 184, "name": "Reconstruct 184", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-184.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["T", "F", "H", "D", "W", "V"], "start_x": 1, "start_y": 3, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "T", "rotation": 0}, "BOTTOM": {"patternId": "V", "rotation": 270}, "FRONT": {"patternId": "F", "rotation": 270}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 180}, "RIGHT": {"patternId": "H", "rotation": 90}}, "bottom_faces": [{"patternId": "V", "rotation": 270, "x": 1, "y": 3}, {"patternId": "H", "rotation": 180, "x": 2, "y": 3}, {"patternId": "D", "rotation": 90, "x": 2, "y": 2}, {"patternId": "T", "rotation": 270, "x": 3, "y": 2}, {"patternId": "W", "rotation": 180, "x": 3, "y": 1}], "slot_sequence": ["RIGHT", "BACK", "TOP", "LEFT"], "required_slots": ["RIGHT", "BACK", "TOP", "LEFT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "T", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 180}, "LEFT": {"patternId": "W", "rotation": 270}, "RIGHT": {"patternId": "H", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "T", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 180}, "LEFT": {"patternId": "W", "rotation": 270}, "RIGHT": {"patternId": "H", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C184\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=H, rotation=180, flipVertical=true\n- step 2: patternId=D, rotation=90, flipVertical=true\n- step 3: patternId=T, rotation=270, flipVertical=true\n- step 4: patternId=W, rotation=180, flipVertical=true\n- allowed patternId values for this task: H, D, T, W, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C184"} +{"sample_id": "C185", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> W -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "W", "E"], "observed_path_faces": [{"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C185_path_sequence.png"}, "metadata": {"level_id": 185, "name": "Reconstruct 185", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-185.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["4", "3", "plus", "8", "C", "H"], "start_x": 3, "start_y": 2, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "4", "rotation": 0}, "BOTTOM": {"patternId": "H", "rotation": 180}, "FRONT": {"patternId": "3", "rotation": 90}, "BACK": {"patternId": "8", "rotation": 0}, "LEFT": {"patternId": "C", "rotation": 0}, "RIGHT": {"patternId": "plus", "rotation": 90}}, "bottom_faces": [{"patternId": "H", "rotation": 180, "x": 3, "y": 2}, {"patternId": "8", "rotation": 180, "x": 3, "y": 1}, {"patternId": "C", "rotation": 180, "x": 2, "y": 1}, {"patternId": "3", "rotation": 270, "x": 1, "y": 1}, {"patternId": "C", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["BACK", "LEFT", "FRONT", "LEFT"], "required_slots": ["BACK", "LEFT", "FRONT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "3", "rotation": 90}, "BACK": {"patternId": "8", "rotation": 180}, "LEFT": {"patternId": "C", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "3", "rotation": 90}, "BACK": {"patternId": "8", "rotation": 180}, "LEFT": {"patternId": "C", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C185\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> W -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=8, rotation=180, flipVertical=true\n- step 2: patternId=C, rotation=180, flipVertical=true\n- step 3: patternId=3, rotation=270, flipVertical=true\n- step 4: patternId=C, rotation=180, flipVertical=true\n- allowed patternId values for this task: 8, C, 3, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C185"} +{"sample_id": "C186", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> S -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "S", "W", "W"], "observed_path_faces": [{"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C186_path_sequence.png"}, "metadata": {"level_id": 186, "name": "Reconstruct 186", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-186.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["G", "N", "arrow_down", "K", "arrow_left", "5"], "start_x": 4, "start_y": 1, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "G", "rotation": 90}, "BOTTOM": {"patternId": "5", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 90}, "LEFT": {"patternId": "arrow_left", "rotation": 0}, "RIGHT": {"patternId": "arrow_down", "rotation": 90}}, "bottom_faces": [{"patternId": "5", "rotation": 0, "x": 4, "y": 1}, {"patternId": "arrow_left", "rotation": 270, "x": 3, "y": 1}, {"patternId": "N", "rotation": 270, "x": 3, "y": 2}, {"patternId": "arrow_down", "rotation": 0, "x": 3, "y": 3}, {"patternId": "G", "rotation": 90, "x": 2, "y": 3}, {"patternId": "arrow_left", "rotation": 90, "x": 1, "y": 3}], "slot_sequence": ["LEFT", "FRONT", "RIGHT", "TOP", "LEFT"], "required_slots": ["LEFT", "FRONT", "RIGHT", "TOP"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "G", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 90}, "RIGHT": {"patternId": "arrow_down", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "G", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 90}, "RIGHT": {"patternId": "arrow_down", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C186\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> S -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_left, rotation=270, flipVertical=true\n- step 2: patternId=N, rotation=270, flipVertical=true\n- step 3: patternId=arrow_down, rotation=0, flipVertical=true\n- step 4: patternId=G, rotation=90, flipVertical=true\n- step 5: patternId=arrow_left, rotation=90, flipVertical=true\n- allowed patternId values for this task: arrow_left, N, arrow_down, G, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C186"} +{"sample_id": "C187", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> E -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "E", "E", "N"], "observed_path_faces": [{"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C187_path_sequence.png"}, "metadata": {"level_id": 187, "name": "Reconstruct 187", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-187.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["1", "4", "O", "U", "star", "N"], "start_x": 1, "start_y": 1, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "1", "rotation": 270}, "BOTTOM": {"patternId": "N", "rotation": 0}, "FRONT": {"patternId": "4", "rotation": 180}, "BACK": {"patternId": "U", "rotation": 180}, "LEFT": {"patternId": "star", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 90}}, "bottom_faces": [{"patternId": "N", "rotation": 0, "x": 1, "y": 1}, {"patternId": "O", "rotation": 180, "x": 2, "y": 1}, {"patternId": "4", "rotation": 270, "x": 2, "y": 2}, {"patternId": "1", "rotation": 0, "x": 3, "y": 2}, {"patternId": "U", "rotation": 90, "x": 4, "y": 2}, {"patternId": "O", "rotation": 0, "x": 4, "y": 1}], "slot_sequence": ["RIGHT", "FRONT", "TOP", "BACK", "RIGHT"], "required_slots": ["RIGHT", "FRONT", "TOP", "BACK"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "1", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "4", "rotation": 180}, "BACK": {"patternId": "U", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "1", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "4", "rotation": 180}, "BACK": {"patternId": "U", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C187\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> E -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=O, rotation=180, flipVertical=true\n- step 2: patternId=4, rotation=270, flipVertical=true\n- step 3: patternId=1, rotation=0, flipVertical=true\n- step 4: patternId=U, rotation=90, flipVertical=true\n- step 5: patternId=O, rotation=0, flipVertical=true\n- allowed patternId values for this task: O, 4, 1, U, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C187"} +{"sample_id": "C188", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> E -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "E", "S", "E"], "observed_path_faces": [{"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C188_path_sequence.png"}, "metadata": {"level_id": 188, "name": "Reconstruct 188", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-188.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["I", "J", "M", "heart", "E", "1"], "start_x": 2, "start_y": 2, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "I", "rotation": 180}, "BOTTOM": {"patternId": "1", "rotation": 90}, "FRONT": {"patternId": "J", "rotation": 270}, "BACK": {"patternId": "heart", "rotation": 180}, "LEFT": {"patternId": "E", "rotation": 180}, "RIGHT": {"patternId": "M", "rotation": 270}}, "bottom_faces": [{"patternId": "1", "rotation": 90, "x": 2, "y": 2}, {"patternId": "E", "rotation": 90, "x": 1, "y": 2}, {"patternId": "heart", "rotation": 90, "x": 1, "y": 1}, {"patternId": "1", "rotation": 180, "x": 2, "y": 1}, {"patternId": "E", "rotation": 180, "x": 2, "y": 2}, {"patternId": "J", "rotation": 270, "x": 3, "y": 2}], "slot_sequence": ["LEFT", "BACK", "BOTTOM", "LEFT", "FRONT"], "required_slots": ["LEFT", "BACK", "BOTTOM", "FRONT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "1", "rotation": 90}, "FRONT": {"patternId": "J", "rotation": 270}, "BACK": {"patternId": "heart", "rotation": 0}, "LEFT": {"patternId": "E", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "1", "rotation": 90}, "FRONT": {"patternId": "J", "rotation": 270}, "BACK": {"patternId": "heart", "rotation": 0}, "LEFT": {"patternId": "E", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C188\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> E -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=E, rotation=90, flipVertical=true\n- step 2: patternId=heart, rotation=90, flipVertical=true\n- step 3: patternId=1, rotation=180, flipVertical=true\n- step 4: patternId=E, rotation=180, flipVertical=true\n- step 5: patternId=J, rotation=270, flipVertical=true\n- allowed patternId values for this task: E, heart, 1, J, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C188"} +{"sample_id": "C189", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> N -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "N", "E", "S"], "observed_path_faces": [{"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C189_path_sequence.png"}, "metadata": {"level_id": 189, "name": "Reconstruct 189", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-189.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["6", "8", "heart", "M", "Z", "C"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "6", "rotation": 90}, "BOTTOM": {"patternId": "C", "rotation": 0}, "FRONT": {"patternId": "8", "rotation": 180}, "BACK": {"patternId": "M", "rotation": 270}, "LEFT": {"patternId": "Z", "rotation": 180}, "RIGHT": {"patternId": "heart", "rotation": 0}}, "bottom_faces": [{"patternId": "C", "rotation": 0, "x": 1, "y": 1}, {"patternId": "8", "rotation": 180, "x": 1, "y": 2}, {"patternId": "C", "rotation": 0, "x": 1, "y": 1}, {"patternId": "heart", "rotation": 90, "x": 2, "y": 1}, {"patternId": "8", "rotation": 270, "x": 2, "y": 2}], "slot_sequence": ["FRONT", "BOTTOM", "RIGHT", "FRONT"], "required_slots": ["FRONT", "BOTTOM", "RIGHT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "C", "rotation": 0}, "FRONT": {"patternId": "8", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "heart", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "C", "rotation": 0}, "FRONT": {"patternId": "8", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "heart", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C189\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): S -> N -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=8, rotation=180, flipVertical=true\n- step 2: patternId=C, rotation=0, flipVertical=true\n- step 3: patternId=heart, rotation=90, flipVertical=true\n- step 4: patternId=8, rotation=270, flipVertical=true\n- allowed patternId values for this task: 8, C, heart, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C189"} +{"sample_id": "C190", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> N -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "N", "S"], "observed_path_faces": [{"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C190_path_sequence.png"}, "metadata": {"level_id": 190, "name": "Reconstruct 190", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-190.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["7", "arrow_down", "I", "Q", "plus", "9"], "start_x": 1, "start_y": 4, "grid_width": 3, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "7", "rotation": 180}, "BOTTOM": {"patternId": "9", "rotation": 0}, "FRONT": {"patternId": "arrow_down", "rotation": 90}, "BACK": {"patternId": "Q", "rotation": 270}, "LEFT": {"patternId": "plus", "rotation": 270}, "RIGHT": {"patternId": "I", "rotation": 270}}, "bottom_faces": [{"patternId": "9", "rotation": 0, "x": 1, "y": 4}, {"patternId": "Q", "rotation": 90, "x": 1, "y": 3}, {"patternId": "7", "rotation": 180, "x": 1, "y": 2}, {"patternId": "arrow_down", "rotation": 90, "x": 1, "y": 1}, {"patternId": "7", "rotation": 180, "x": 1, "y": 2}], "slot_sequence": ["BACK", "TOP", "FRONT", "TOP"], "required_slots": ["BACK", "TOP", "FRONT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "7", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_down", "rotation": 90}, "BACK": {"patternId": "Q", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "7", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_down", "rotation": 90}, "BACK": {"patternId": "Q", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C190\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> N -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Q, rotation=90, flipVertical=true\n- step 2: patternId=7, rotation=180, flipVertical=true\n- step 3: patternId=arrow_down, rotation=90, flipVertical=true\n- step 4: patternId=7, rotation=180, flipVertical=true\n- allowed patternId values for this task: Q, 7, arrow_down, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C190"} +{"sample_id": "C191", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "S", "W"], "observed_path_faces": [{"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C191_path_sequence.png"}, "metadata": {"level_id": 191, "name": "Reconstruct 191", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-191.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_left", "smile", "K", "I", "M", "U"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "arrow_left", "rotation": 90}, "BOTTOM": {"patternId": "U", "rotation": 180}, "FRONT": {"patternId": "smile", "rotation": 270}, "BACK": {"patternId": "I", "rotation": 0}, "LEFT": {"patternId": "M", "rotation": 90}, "RIGHT": {"patternId": "K", "rotation": 270}}, "bottom_faces": [{"patternId": "U", "rotation": 180, "x": 3, "y": 1}, {"patternId": "smile", "rotation": 270, "x": 3, "y": 2}, {"patternId": "M", "rotation": 90, "x": 2, "y": 2}, {"patternId": "arrow_left", "rotation": 0, "x": 2, "y": 3}, {"patternId": "I", "rotation": 90, "x": 1, "y": 3}], "slot_sequence": ["FRONT", "LEFT", "TOP", "BACK"], "required_slots": ["FRONT", "LEFT", "TOP", "BACK"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "arrow_left", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "smile", "rotation": 270}, "BACK": {"patternId": "I", "rotation": 180}, "LEFT": {"patternId": "M", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "arrow_left", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "smile", "rotation": 270}, "BACK": {"patternId": "I", "rotation": 180}, "LEFT": {"patternId": "M", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C191\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=smile, rotation=270, flipVertical=true\n- step 2: patternId=M, rotation=90, flipVertical=true\n- step 3: patternId=arrow_left, rotation=0, flipVertical=true\n- step 4: patternId=I, rotation=90, flipVertical=true\n- allowed patternId values for this task: smile, M, arrow_left, I, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C191"} +{"sample_id": "C192", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> N -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "N", "N", "N"], "observed_path_faces": [{"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C192_path_sequence.png"}, "metadata": {"level_id": 192, "name": "Reconstruct 192", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-192.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["8", "P", "diamond", "star", "8", "arrow_right"], "start_x": 3, "start_y": 4, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "8", "rotation": 270}, "BOTTOM": {"patternId": "arrow_right", "rotation": 90}, "FRONT": {"patternId": "P", "rotation": 90}, "BACK": {"patternId": "star", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 0}, "RIGHT": {"patternId": "diamond", "rotation": 90}}, "bottom_faces": [{"patternId": "arrow_right", "rotation": 90, "x": 3, "y": 4}, {"patternId": "8", "rotation": 270, "x": 2, "y": 4}, {"patternId": "8", "rotation": 90, "x": 1, "y": 4}, {"patternId": "star", "rotation": 0, "x": 1, "y": 3}, {"patternId": "arrow_right", "rotation": 270, "x": 1, "y": 2}, {"patternId": "P", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "TOP", "BACK", "BOTTOM", "FRONT"], "required_slots": ["LEFT", "TOP", "BACK", "BOTTOM", "FRONT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "8", "rotation": 270}, "BOTTOM": {"patternId": "arrow_right", "rotation": 90}, "FRONT": {"patternId": "P", "rotation": 90}, "BACK": {"patternId": "star", "rotation": 180}, "LEFT": {"patternId": "8", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "8", "rotation": 270}, "BOTTOM": {"patternId": "arrow_right", "rotation": 90}, "FRONT": {"patternId": "P", "rotation": 90}, "BACK": {"patternId": "star", "rotation": 180}, "LEFT": {"patternId": "8", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C192\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> N -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=8, rotation=270, flipVertical=true\n- step 2: patternId=8, rotation=90, flipVertical=true\n- step 3: patternId=star, rotation=0, flipVertical=true\n- step 4: patternId=arrow_right, rotation=270, flipVertical=true\n- step 5: patternId=P, rotation=270, flipVertical=true\n- allowed patternId values for this task: 8, star, arrow_right, P, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C192"} +{"sample_id": "C193", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> S -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "S", "E", "N"], "observed_path_faces": [{"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C193_path_sequence.png"}, "metadata": {"level_id": 193, "name": "Reconstruct 193", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-193.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["F", "5", "I", "arrow_right", "triangle", "I"], "start_x": 1, "start_y": 2, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "F", "rotation": 180}, "BOTTOM": {"patternId": "I", "rotation": 270}, "FRONT": {"patternId": "5", "rotation": 90}, "BACK": {"patternId": "arrow_right", "rotation": 270}, "LEFT": {"patternId": "triangle", "rotation": 180}, "RIGHT": {"patternId": "I", "rotation": 180}}, "bottom_faces": [{"patternId": "I", "rotation": 270, "x": 1, "y": 2}, {"patternId": "arrow_right", "rotation": 90, "x": 1, "y": 1}, {"patternId": "I", "rotation": 0, "x": 2, "y": 1}, {"patternId": "I", "rotation": 0, "x": 2, "y": 2}, {"patternId": "5", "rotation": 180, "x": 3, "y": 2}, {"patternId": "I", "rotation": 270, "x": 3, "y": 1}], "slot_sequence": ["BACK", "RIGHT", "BOTTOM", "FRONT", "RIGHT"], "required_slots": ["BACK", "RIGHT", "BOTTOM", "FRONT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "I", "rotation": 270}, "FRONT": {"patternId": "5", "rotation": 90}, "BACK": {"patternId": "arrow_right", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "I", "rotation": 270}, "FRONT": {"patternId": "5", "rotation": 90}, "BACK": {"patternId": "arrow_right", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C193\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> S -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_right, rotation=90, flipVertical=true\n- step 2: patternId=I, rotation=0, flipVertical=true\n- step 3: patternId=I, rotation=0, flipVertical=true\n- step 4: patternId=5, rotation=180, flipVertical=true\n- step 5: patternId=I, rotation=270, flipVertical=true\n- allowed patternId values for this task: arrow_right, I, 5, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C193"} +{"sample_id": "C194", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "N", "E"], "observed_path_faces": [{"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C194_path_sequence.png"}, "metadata": {"level_id": 194, "name": "Reconstruct 194", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-194.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Z", "1", "G", "arrow_up", "arrow_right", "R"], "start_x": 2, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "Z", "rotation": 180}, "BOTTOM": {"patternId": "R", "rotation": 180}, "FRONT": {"patternId": "1", "rotation": 0}, "BACK": {"patternId": "arrow_up", "rotation": 0}, "LEFT": {"patternId": "arrow_right", "rotation": 0}, "RIGHT": {"patternId": "G", "rotation": 180}}, "bottom_faces": [{"patternId": "R", "rotation": 180, "x": 2, "y": 3}, {"patternId": "arrow_right", "rotation": 270, "x": 1, "y": 3}, {"patternId": "arrow_up", "rotation": 270, "x": 1, "y": 2}, {"patternId": "G", "rotation": 90, "x": 1, "y": 1}, {"patternId": "R", "rotation": 0, "x": 2, "y": 1}], "slot_sequence": ["LEFT", "BACK", "RIGHT", "BOTTOM"], "required_slots": ["LEFT", "BACK", "RIGHT", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "R", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_up", "rotation": 180}, "LEFT": {"patternId": "arrow_right", "rotation": 90}, "RIGHT": {"patternId": "G", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "R", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_up", "rotation": 180}, "LEFT": {"patternId": "arrow_right", "rotation": 90}, "RIGHT": {"patternId": "G", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C194\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_right, rotation=270, flipVertical=true\n- step 2: patternId=arrow_up, rotation=270, flipVertical=true\n- step 3: patternId=G, rotation=90, flipVertical=true\n- step 4: patternId=R, rotation=0, flipVertical=true\n- allowed patternId values for this task: arrow_right, arrow_up, G, R, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C194"} +{"sample_id": "C195", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "E", "S"], "observed_path_faces": [{"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C195_path_sequence.png"}, "metadata": {"level_id": 195, "name": "Reconstruct 195", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-195.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["W", "1", "plus", "G", "S", "V"], "start_x": 1, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "W", "rotation": 0}, "BOTTOM": {"patternId": "V", "rotation": 180}, "FRONT": {"patternId": "1", "rotation": 180}, "BACK": {"patternId": "G", "rotation": 90}, "LEFT": {"patternId": "S", "rotation": 90}, "RIGHT": {"patternId": "plus", "rotation": 0}}, "bottom_faces": [{"patternId": "V", "rotation": 180, "x": 1, "y": 3}, {"patternId": "G", "rotation": 270, "x": 1, "y": 2}, {"patternId": "W", "rotation": 0, "x": 1, "y": 1}, {"patternId": "plus", "rotation": 270, "x": 2, "y": 1}, {"patternId": "G", "rotation": 0, "x": 2, "y": 2}], "slot_sequence": ["BACK", "TOP", "RIGHT", "BACK"], "required_slots": ["BACK", "TOP", "RIGHT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "W", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "G", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "plus", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "W", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "G", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "plus", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C195\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=G, rotation=270, flipVertical=true\n- step 2: patternId=W, rotation=0, flipVertical=true\n- step 3: patternId=plus, rotation=270, flipVertical=true\n- step 4: patternId=G, rotation=0, flipVertical=true\n- allowed patternId values for this task: G, W, plus, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C195"} +{"sample_id": "C196", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "S", "S"], "observed_path_faces": [{"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C196_path_sequence.png"}, "metadata": {"level_id": 196, "name": "Reconstruct 196", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-196.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["I", "D", "D", "Q", "X", "X"], "start_x": 2, "start_y": 2, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "I", "rotation": 270}, "BOTTOM": {"patternId": "X", "rotation": 270}, "FRONT": {"patternId": "D", "rotation": 90}, "BACK": {"patternId": "Q", "rotation": 270}, "LEFT": {"patternId": "X", "rotation": 90}, "RIGHT": {"patternId": "D", "rotation": 270}}, "bottom_faces": [{"patternId": "X", "rotation": 270, "x": 2, "y": 2}, {"patternId": "X", "rotation": 0, "x": 1, "y": 2}, {"patternId": "Q", "rotation": 180, "x": 1, "y": 1}, {"patternId": "X", "rotation": 0, "x": 1, "y": 2}, {"patternId": "D", "rotation": 0, "x": 1, "y": 3}], "slot_sequence": ["LEFT", "BACK", "LEFT", "FRONT"], "required_slots": ["LEFT", "BACK", "FRONT"], "required_count": 3, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 90}, "BACK": {"patternId": "Q", "rotation": 90}, "LEFT": {"patternId": "X", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 90}, "BACK": {"patternId": "Q", "rotation": 90}, "LEFT": {"patternId": "X", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C196\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=X, rotation=0, flipVertical=true\n- step 2: patternId=Q, rotation=180, flipVertical=true\n- step 3: patternId=X, rotation=0, flipVertical=true\n- step 4: patternId=D, rotation=0, flipVertical=true\n- allowed patternId values for this task: X, Q, D, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C196"} +{"sample_id": "C197", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "N", "N"], "observed_path_faces": [{"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C197_path_sequence.png"}, "metadata": {"level_id": 197, "name": "Reconstruct 197", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-197.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["T", "I", "7", "5", "3", "arrow_up"], "start_x": 1, "start_y": 4, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "T", "rotation": 90}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "I", "rotation": 90}, "BACK": {"patternId": "5", "rotation": 90}, "LEFT": {"patternId": "3", "rotation": 0}, "RIGHT": {"patternId": "7", "rotation": 180}}, "bottom_faces": [{"patternId": "arrow_up", "rotation": 270, "x": 1, "y": 4}, {"patternId": "5", "rotation": 270, "x": 1, "y": 3}, {"patternId": "7", "rotation": 0, "x": 2, "y": 3}, {"patternId": "T", "rotation": 0, "x": 2, "y": 2}, {"patternId": "3", "rotation": 0, "x": 2, "y": 1}], "slot_sequence": ["BACK", "RIGHT", "TOP", "LEFT"], "required_slots": ["BACK", "RIGHT", "TOP", "LEFT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "T", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "5", "rotation": 270}, "LEFT": {"patternId": "3", "rotation": 90}, "RIGHT": {"patternId": "7", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "T", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "5", "rotation": 270}, "LEFT": {"patternId": "3", "rotation": 90}, "RIGHT": {"patternId": "7", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C197\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=5, rotation=270, flipVertical=true\n- step 2: patternId=7, rotation=0, flipVertical=true\n- step 3: patternId=T, rotation=0, flipVertical=true\n- step 4: patternId=3, rotation=0, flipVertical=true\n- allowed patternId values for this task: 5, 7, T, 3, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C197"} +{"sample_id": "C198", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> S -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "S", "E", "S"], "observed_path_faces": [{"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C198_path_sequence.png"}, "metadata": {"level_id": 198, "name": "Reconstruct 198", "difficulty": 2, "move_count": 5, "tier": 2, "source_level_path": "levels/reconstruct/generated-198.json", "tier_label": "Difficulty 2"}, "description": "5-move reconstruct puzzle", "net_faces": [{"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["square", "arrow_right", "F", "Z", "9", "circle"], "start_x": 1, "start_y": 2, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "square", "rotation": 270}, "BOTTOM": {"patternId": "circle", "rotation": 90}, "FRONT": {"patternId": "arrow_right", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "9", "rotation": 270}, "RIGHT": {"patternId": "F", "rotation": 180}}, "bottom_faces": [{"patternId": "circle", "rotation": 90, "x": 1, "y": 2}, {"patternId": "F", "rotation": 270, "x": 2, "y": 2}, {"patternId": "Z", "rotation": 180, "x": 2, "y": 1}, {"patternId": "F", "rotation": 270, "x": 2, "y": 2}, {"patternId": "square", "rotation": 90, "x": 3, "y": 2}, {"patternId": "arrow_right", "rotation": 0, "x": 3, "y": 3}], "slot_sequence": ["RIGHT", "BACK", "RIGHT", "TOP", "FRONT"], "required_slots": ["RIGHT", "BACK", "TOP", "FRONT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "square", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_right", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "F", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "square", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_right", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "F", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C198\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> S -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=F, rotation=270, flipVertical=true\n- step 2: patternId=Z, rotation=180, flipVertical=true\n- step 3: patternId=F, rotation=270, flipVertical=true\n- step 4: patternId=square, rotation=90, flipVertical=true\n- step 5: patternId=arrow_right, rotation=0, flipVertical=true\n- allowed patternId values for this task: F, Z, square, arrow_right, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C198"} +{"sample_id": "C199", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "W", "W"], "observed_path_faces": [{"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C199_path_sequence.png"}, "metadata": {"level_id": 199, "name": "Reconstruct 199", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-199.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["4", "circle", "heart", "B", "F", "M"], "start_x": 2, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "4", "rotation": 90}, "BOTTOM": {"patternId": "M", "rotation": 270}, "FRONT": {"patternId": "circle", "rotation": 180}, "BACK": {"patternId": "B", "rotation": 180}, "LEFT": {"patternId": "F", "rotation": 90}, "RIGHT": {"patternId": "heart", "rotation": 0}}, "bottom_faces": [{"patternId": "M", "rotation": 270, "x": 2, "y": 1}, {"patternId": "heart", "rotation": 90, "x": 3, "y": 1}, {"patternId": "circle", "rotation": 270, "x": 3, "y": 2}, {"patternId": "M", "rotation": 0, "x": 2, "y": 2}, {"patternId": "B", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["RIGHT", "FRONT", "BOTTOM", "BACK"], "required_slots": ["RIGHT", "FRONT", "BOTTOM", "BACK"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "M", "rotation": 270}, "FRONT": {"patternId": "circle", "rotation": 180}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "heart", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "M", "rotation": 270}, "FRONT": {"patternId": "circle", "rotation": 180}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "heart", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C199\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=heart, rotation=90, flipVertical=true\n- step 2: patternId=circle, rotation=270, flipVertical=true\n- step 3: patternId=M, rotation=0, flipVertical=true\n- step 4: patternId=B, rotation=90, flipVertical=true\n- allowed patternId values for this task: heart, circle, M, B, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C199"} +{"sample_id": "C200", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "S", "W"], "observed_path_faces": [{"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C200_path_sequence.png"}, "metadata": {"level_id": 200, "name": "Reconstruct 200", "difficulty": 2, "move_count": 4, "tier": 2, "source_level_path": "levels/reconstruct/generated-200.json", "tier_label": "Difficulty 2"}, "description": "4-move reconstruct puzzle", "net_faces": [{"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["U", "L", "E", "star", "Y", "Z"], "start_x": 4, "start_y": 1, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "U", "rotation": 0}, "BOTTOM": {"patternId": "Z", "rotation": 0}, "FRONT": {"patternId": "L", "rotation": 270}, "BACK": {"patternId": "star", "rotation": 90}, "LEFT": {"patternId": "Y", "rotation": 180}, "RIGHT": {"patternId": "E", "rotation": 90}}, "bottom_faces": [{"patternId": "Z", "rotation": 0, "x": 4, "y": 1}, {"patternId": "Y", "rotation": 90, "x": 3, "y": 1}, {"patternId": "U", "rotation": 180, "x": 2, "y": 1}, {"patternId": "L", "rotation": 90, "x": 2, "y": 2}, {"patternId": "E", "rotation": 270, "x": 1, "y": 2}], "slot_sequence": ["LEFT", "TOP", "FRONT", "RIGHT"], "required_slots": ["LEFT", "TOP", "FRONT", "RIGHT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "U", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "L", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 270}, "RIGHT": {"patternId": "E", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "U", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "L", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 270}, "RIGHT": {"patternId": "E", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C200\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Y, rotation=90, flipVertical=true\n- step 2: patternId=U, rotation=180, flipVertical=true\n- step 3: patternId=L, rotation=90, flipVertical=true\n- step 4: patternId=E, rotation=270, flipVertical=true\n- allowed patternId values for this task: Y, U, L, E, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C200"} +{"sample_id": "C201", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> S -> W -> N -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "S", "W", "N", "N", "E"], "observed_path_faces": [{"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C201_path_sequence.png"}, "metadata": {"level_id": 201, "name": "Reconstruct 201", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-201.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["star", "heart", "diamond", "arrow_up", "N", "1"], "start_x": 3, "start_y": 3, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "star", "rotation": 90}, "BOTTOM": {"patternId": "1", "rotation": 90}, "FRONT": {"patternId": "heart", "rotation": 180}, "BACK": {"patternId": "arrow_up", "rotation": 90}, "LEFT": {"patternId": "N", "rotation": 270}, "RIGHT": {"patternId": "diamond", "rotation": 270}}, "bottom_faces": [{"patternId": "1", "rotation": 90, "x": 3, "y": 3}, {"patternId": "arrow_up", "rotation": 270, "x": 3, "y": 2}, {"patternId": "N", "rotation": 90, "x": 2, "y": 2}, {"patternId": "1", "rotation": 0, "x": 2, "y": 3}, {"patternId": "heart", "rotation": 90, "x": 1, "y": 3}, {"patternId": "N", "rotation": 180, "x": 1, "y": 2}, {"patternId": "arrow_up", "rotation": 0, "x": 1, "y": 1}, {"patternId": "1", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["BACK", "LEFT", "BOTTOM", "FRONT", "LEFT", "BACK", "BOTTOM"], "required_slots": ["BACK", "LEFT", "BOTTOM", "FRONT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "1", "rotation": 90}, "FRONT": {"patternId": "heart", "rotation": 180}, "BACK": {"patternId": "arrow_up", "rotation": 270}, "LEFT": {"patternId": "N", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "1", "rotation": 90}, "FRONT": {"patternId": "heart", "rotation": 180}, "BACK": {"patternId": "arrow_up", "rotation": 270}, "LEFT": {"patternId": "N", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C201\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> S -> W -> N -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_up, rotation=270, flipVertical=true\n- step 2: patternId=N, rotation=90, flipVertical=true\n- step 3: patternId=1, rotation=0, flipVertical=true\n- step 4: patternId=heart, rotation=90, flipVertical=true\n- step 5: patternId=N, rotation=180, flipVertical=true\n- step 6: patternId=arrow_up, rotation=0, flipVertical=true\n- step 7: patternId=1, rotation=180, flipVertical=true\n- allowed patternId values for this task: arrow_up, N, 1, heart, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C201"} +{"sample_id": "C202", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> S -> W -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "S", "W", "S", "E"], "observed_path_faces": [{"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C202_path_sequence.png"}, "metadata": {"level_id": 202, "name": "Reconstruct 202", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-202.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["6", "6", "7", "arrow_down", "N", "X"], "start_x": 3, "start_y": 2, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "6", "rotation": 270}, "BOTTOM": {"patternId": "X", "rotation": 180}, "FRONT": {"patternId": "6", "rotation": 180}, "BACK": {"patternId": "arrow_down", "rotation": 0}, "LEFT": {"patternId": "N", "rotation": 0}, "RIGHT": {"patternId": "7", "rotation": 180}}, "bottom_faces": [{"patternId": "X", "rotation": 180, "x": 3, "y": 2}, {"patternId": "arrow_down", "rotation": 180, "x": 3, "y": 1}, {"patternId": "N", "rotation": 180, "x": 2, "y": 1}, {"patternId": "X", "rotation": 90, "x": 2, "y": 2}, {"patternId": "6", "rotation": 90, "x": 1, "y": 2}, {"patternId": "7", "rotation": 90, "x": 1, "y": 3}, {"patternId": "X", "rotation": 0, "x": 2, "y": 3}], "slot_sequence": ["BACK", "LEFT", "BOTTOM", "FRONT", "RIGHT", "BOTTOM"], "required_slots": ["BACK", "LEFT", "BOTTOM", "FRONT", "RIGHT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "X", "rotation": 180}, "FRONT": {"patternId": "6", "rotation": 180}, "BACK": {"patternId": "arrow_down", "rotation": 180}, "LEFT": {"patternId": "N", "rotation": 90}, "RIGHT": {"patternId": "7", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "X", "rotation": 180}, "FRONT": {"patternId": "6", "rotation": 180}, "BACK": {"patternId": "arrow_down", "rotation": 180}, "LEFT": {"patternId": "N", "rotation": 90}, "RIGHT": {"patternId": "7", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C202\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> S -> W -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_down, rotation=180, flipVertical=true\n- step 2: patternId=N, rotation=180, flipVertical=true\n- step 3: patternId=X, rotation=90, flipVertical=true\n- step 4: patternId=6, rotation=90, flipVertical=true\n- step 5: patternId=7, rotation=90, flipVertical=true\n- step 6: patternId=X, rotation=0, flipVertical=true\n- allowed patternId values for this task: arrow_down, N, X, 6, 7, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C202"} +{"sample_id": "C203", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> E -> W -> N -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "E", "W", "N", "W", "S"], "observed_path_faces": [{"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C203_path_sequence.png"}, "metadata": {"level_id": 203, "name": "Reconstruct 203", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-203.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["2", "O", "1", "circle", "J", "Q"], "start_x": 3, "start_y": 2, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "2", "rotation": 180}, "BOTTOM": {"patternId": "Q", "rotation": 90}, "FRONT": {"patternId": "O", "rotation": 180}, "BACK": {"patternId": "circle", "rotation": 180}, "LEFT": {"patternId": "J", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 0}}, "bottom_faces": [{"patternId": "Q", "rotation": 90, "x": 3, "y": 2}, {"patternId": "J", "rotation": 270, "x": 2, "y": 2}, {"patternId": "Q", "rotation": 90, "x": 3, "y": 2}, {"patternId": "J", "rotation": 270, "x": 2, "y": 2}, {"patternId": "circle", "rotation": 90, "x": 2, "y": 1}, {"patternId": "2", "rotation": 270, "x": 1, "y": 1}, {"patternId": "J", "rotation": 180, "x": 1, "y": 2}], "slot_sequence": ["LEFT", "BOTTOM", "LEFT", "BACK", "TOP", "LEFT"], "required_slots": ["LEFT", "BOTTOM", "BACK", "TOP"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "2", "rotation": 180}, "BOTTOM": {"patternId": "Q", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 0}, "LEFT": {"patternId": "J", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "2", "rotation": 180}, "BOTTOM": {"patternId": "Q", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 0}, "LEFT": {"patternId": "J", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C203\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): W -> E -> W -> N -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=J, rotation=270, flipVertical=true\n- step 2: patternId=Q, rotation=90, flipVertical=true\n- step 3: patternId=J, rotation=270, flipVertical=true\n- step 4: patternId=circle, rotation=90, flipVertical=true\n- step 5: patternId=2, rotation=270, flipVertical=true\n- step 6: patternId=J, rotation=180, flipVertical=true\n- allowed patternId values for this task: J, Q, circle, 2, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C203"} +{"sample_id": "C204", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> S -> E -> S -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "S", "E", "S", "W", "W"], "observed_path_faces": [{"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C204_path_sequence.png"}, "metadata": {"level_id": 204, "name": "Reconstruct 204", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-204.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["8", "E", "R", "2", "N", "2"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "8", "rotation": 0}, "BOTTOM": {"patternId": "2", "rotation": 180}, "FRONT": {"patternId": "E", "rotation": 180}, "BACK": {"patternId": "2", "rotation": 90}, "LEFT": {"patternId": "N", "rotation": 180}, "RIGHT": {"patternId": "R", "rotation": 0}}, "bottom_faces": [{"patternId": "2", "rotation": 180, "x": 1, "y": 1}, {"patternId": "R", "rotation": 90, "x": 2, "y": 1}, {"patternId": "E", "rotation": 270, "x": 2, "y": 2}, {"patternId": "N", "rotation": 270, "x": 2, "y": 3}, {"patternId": "8", "rotation": 0, "x": 3, "y": 3}, {"patternId": "2", "rotation": 270, "x": 3, "y": 4}, {"patternId": "N", "rotation": 0, "x": 2, "y": 4}, {"patternId": "E", "rotation": 0, "x": 1, "y": 4}], "slot_sequence": ["RIGHT", "FRONT", "LEFT", "TOP", "BACK", "LEFT", "FRONT"], "required_slots": ["RIGHT", "FRONT", "LEFT", "TOP", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "8", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "E", "rotation": 180}, "BACK": {"patternId": "2", "rotation": 270}, "LEFT": {"patternId": "N", "rotation": 270}, "RIGHT": {"patternId": "R", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "8", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "E", "rotation": 180}, "BACK": {"patternId": "2", "rotation": 270}, "LEFT": {"patternId": "N", "rotation": 270}, "RIGHT": {"patternId": "R", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C204\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> S -> E -> S -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=R, rotation=90, flipVertical=true\n- step 2: patternId=E, rotation=270, flipVertical=true\n- step 3: patternId=N, rotation=270, flipVertical=true\n- step 4: patternId=8, rotation=0, flipVertical=true\n- step 5: patternId=2, rotation=270, flipVertical=true\n- step 6: patternId=N, rotation=0, flipVertical=true\n- step 7: patternId=E, rotation=0, flipVertical=true\n- allowed patternId values for this task: R, E, N, 8, 2, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C204"} +{"sample_id": "C205", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> W -> N -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "W", "N", "E", "N"], "observed_path_faces": [{"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C205_path_sequence.png"}, "metadata": {"level_id": 205, "name": "Reconstruct 205", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-205.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["I", "3", "heart", "arrow_up", "1", "diamond"], "start_x": 3, "start_y": 2, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "I", "rotation": 0}, "BOTTOM": {"patternId": "diamond", "rotation": 90}, "FRONT": {"patternId": "3", "rotation": 0}, "BACK": {"patternId": "arrow_up", "rotation": 0}, "LEFT": {"patternId": "1", "rotation": 0}, "RIGHT": {"patternId": "heart", "rotation": 270}}, "bottom_faces": [{"patternId": "diamond", "rotation": 90, "x": 3, "y": 2}, {"patternId": "1", "rotation": 270, "x": 2, "y": 2}, {"patternId": "3", "rotation": 270, "x": 2, "y": 3}, {"patternId": "I", "rotation": 270, "x": 1, "y": 3}, {"patternId": "1", "rotation": 0, "x": 1, "y": 2}, {"patternId": "3", "rotation": 0, "x": 2, "y": 2}, {"patternId": "diamond", "rotation": 90, "x": 2, "y": 1}], "slot_sequence": ["LEFT", "FRONT", "TOP", "LEFT", "FRONT", "BOTTOM"], "required_slots": ["LEFT", "FRONT", "TOP", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "I", "rotation": 0}, "BOTTOM": {"patternId": "diamond", "rotation": 90}, "FRONT": {"patternId": "3", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "1", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 0}, "BOTTOM": {"patternId": "diamond", "rotation": 90}, "FRONT": {"patternId": "3", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "1", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C205\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> W -> N -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=1, rotation=270, flipVertical=true\n- step 2: patternId=3, rotation=270, flipVertical=true\n- step 3: patternId=I, rotation=270, flipVertical=true\n- step 4: patternId=1, rotation=0, flipVertical=true\n- step 5: patternId=3, rotation=0, flipVertical=true\n- step 6: patternId=diamond, rotation=90, flipVertical=true\n- allowed patternId values for this task: 1, 3, I, diamond, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C205"} +{"sample_id": "C206", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> E -> N -> W -> N -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "E", "N", "W", "N", "E", "S"], "observed_path_faces": [{"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C206_path_sequence.png"}, "metadata": {"level_id": 206, "name": "Reconstruct 206", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-206.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Y", "I", "X", "arrow_left", "P", "arrow_right"], "start_x": 2, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "Y", "rotation": 180}, "BOTTOM": {"patternId": "arrow_right", "rotation": 90}, "FRONT": {"patternId": "I", "rotation": 180}, "BACK": {"patternId": "arrow_left", "rotation": 0}, "LEFT": {"patternId": "P", "rotation": 0}, "RIGHT": {"patternId": "X", "rotation": 0}}, "bottom_faces": [{"patternId": "arrow_right", "rotation": 90, "x": 2, "y": 3}, {"patternId": "P", "rotation": 270, "x": 1, "y": 3}, {"patternId": "arrow_right", "rotation": 90, "x": 2, "y": 3}, {"patternId": "arrow_left", "rotation": 180, "x": 2, "y": 2}, {"patternId": "P", "rotation": 180, "x": 1, "y": 2}, {"patternId": "Y", "rotation": 270, "x": 1, "y": 1}, {"patternId": "arrow_left", "rotation": 270, "x": 2, "y": 1}, {"patternId": "P", "rotation": 270, "x": 2, "y": 2}], "slot_sequence": ["LEFT", "BOTTOM", "BACK", "LEFT", "TOP", "BACK", "LEFT"], "required_slots": ["LEFT", "BOTTOM", "BACK", "TOP"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "Y", "rotation": 180}, "BOTTOM": {"patternId": "arrow_right", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 180}, "LEFT": {"patternId": "P", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "Y", "rotation": 180}, "BOTTOM": {"patternId": "arrow_right", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 180}, "LEFT": {"patternId": "P", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C206\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): W -> E -> N -> W -> N -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=P, rotation=270, flipVertical=true\n- step 2: patternId=arrow_right, rotation=90, flipVertical=true\n- step 3: patternId=arrow_left, rotation=180, flipVertical=true\n- step 4: patternId=P, rotation=180, flipVertical=true\n- step 5: patternId=Y, rotation=270, flipVertical=true\n- step 6: patternId=arrow_left, rotation=270, flipVertical=true\n- step 7: patternId=P, rotation=270, flipVertical=true\n- allowed patternId values for this task: P, arrow_right, arrow_left, Y, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C206"} +{"sample_id": "C207", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> N -> N -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "N", "N", "W", "N"], "observed_path_faces": [{"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C207_path_sequence.png"}, "metadata": {"level_id": 207, "name": "Reconstruct 207", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-207.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["M", "J", "Z", "E", "D", "arrow_down"], "start_x": 3, "start_y": 5, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "M", "rotation": 90}, "BOTTOM": {"patternId": "arrow_down", "rotation": 270}, "FRONT": {"patternId": "J", "rotation": 0}, "BACK": {"patternId": "E", "rotation": 180}, "LEFT": {"patternId": "D", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 180}}, "bottom_faces": [{"patternId": "arrow_down", "rotation": 270, "x": 3, "y": 5}, {"patternId": "E", "rotation": 0, "x": 3, "y": 4}, {"patternId": "D", "rotation": 180, "x": 2, "y": 4}, {"patternId": "M", "rotation": 180, "x": 2, "y": 3}, {"patternId": "Z", "rotation": 180, "x": 2, "y": 2}, {"patternId": "J", "rotation": 0, "x": 1, "y": 2}, {"patternId": "arrow_down", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["BACK", "LEFT", "TOP", "RIGHT", "FRONT", "BOTTOM"], "required_slots": ["BACK", "LEFT", "TOP", "RIGHT", "FRONT", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "M", "rotation": 90}, "BOTTOM": {"patternId": "arrow_down", "rotation": 270}, "FRONT": {"patternId": "J", "rotation": 0}, "BACK": {"patternId": "E", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 90}, "RIGHT": {"patternId": "Z", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 90}, "BOTTOM": {"patternId": "arrow_down", "rotation": 270}, "FRONT": {"patternId": "J", "rotation": 0}, "BACK": {"patternId": "E", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 90}, "RIGHT": {"patternId": "Z", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C207\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> N -> N -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=E, rotation=0, flipVertical=true\n- step 2: patternId=D, rotation=180, flipVertical=true\n- step 3: patternId=M, rotation=180, flipVertical=true\n- step 4: patternId=Z, rotation=180, flipVertical=true\n- step 5: patternId=J, rotation=0, flipVertical=true\n- step 6: patternId=arrow_down, rotation=270, flipVertical=true\n- allowed patternId values for this task: E, D, M, Z, J, arrow_down, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C207"} +{"sample_id": "C208", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> E -> E -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "E", "E", "N", "E"], "observed_path_faces": [{"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C208_path_sequence.png"}, "metadata": {"level_id": 208, "name": "Reconstruct 208", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-208.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["O", "circle", "circle", "6", "Y", "F"], "start_x": 1, "start_y": 1, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "O", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 0}, "FRONT": {"patternId": "circle", "rotation": 90}, "BACK": {"patternId": "6", "rotation": 270}, "LEFT": {"patternId": "Y", "rotation": 90}, "RIGHT": {"patternId": "circle", "rotation": 270}}, "bottom_faces": [{"patternId": "F", "rotation": 0, "x": 1, "y": 1}, {"patternId": "circle", "rotation": 90, "x": 1, "y": 2}, {"patternId": "O", "rotation": 0, "x": 1, "y": 3}, {"patternId": "circle", "rotation": 180, "x": 2, "y": 3}, {"patternId": "F", "rotation": 180, "x": 3, "y": 3}, {"patternId": "circle", "rotation": 270, "x": 3, "y": 2}, {"patternId": "Y", "rotation": 270, "x": 4, "y": 2}], "slot_sequence": ["FRONT", "TOP", "RIGHT", "BOTTOM", "FRONT", "LEFT"], "required_slots": ["FRONT", "TOP", "RIGHT", "BOTTOM", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "O", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 0}, "FRONT": {"patternId": "circle", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 180}, "RIGHT": {"patternId": "circle", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 0}, "FRONT": {"patternId": "circle", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 180}, "RIGHT": {"patternId": "circle", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C208\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> E -> E -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=circle, rotation=90, flipVertical=true\n- step 2: patternId=O, rotation=0, flipVertical=true\n- step 3: patternId=circle, rotation=180, flipVertical=true\n- step 4: patternId=F, rotation=180, flipVertical=true\n- step 5: patternId=circle, rotation=270, flipVertical=true\n- step 6: patternId=Y, rotation=270, flipVertical=true\n- allowed patternId values for this task: circle, O, F, Y, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C208"} +{"sample_id": "C209", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> W -> S -> E -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "W", "S", "E", "N", "N"], "observed_path_faces": [{"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C209_path_sequence.png"}, "metadata": {"level_id": 209, "name": "Reconstruct 209", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-209.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["K", "2", "3", "B", "O", "3"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "K", "rotation": 0}, "BOTTOM": {"patternId": "3", "rotation": 90}, "FRONT": {"patternId": "2", "rotation": 180}, "BACK": {"patternId": "B", "rotation": 180}, "LEFT": {"patternId": "O", "rotation": 180}, "RIGHT": {"patternId": "3", "rotation": 270}}, "bottom_faces": [{"patternId": "3", "rotation": 90, "x": 3, "y": 1}, {"patternId": "O", "rotation": 90, "x": 2, "y": 1}, {"patternId": "2", "rotation": 90, "x": 2, "y": 2}, {"patternId": "K", "rotation": 270, "x": 1, "y": 2}, {"patternId": "3", "rotation": 90, "x": 1, "y": 3}, {"patternId": "2", "rotation": 0, "x": 2, "y": 3}, {"patternId": "K", "rotation": 180, "x": 2, "y": 2}, {"patternId": "B", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["LEFT", "FRONT", "TOP", "RIGHT", "FRONT", "TOP", "BACK"], "required_slots": ["LEFT", "FRONT", "TOP", "RIGHT", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "K", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 180}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 270}, "RIGHT": {"patternId": "3", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "K", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 180}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 270}, "RIGHT": {"patternId": "3", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C209\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> W -> S -> E -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=O, rotation=90, flipVertical=true\n- step 2: patternId=2, rotation=90, flipVertical=true\n- step 3: patternId=K, rotation=270, flipVertical=true\n- step 4: patternId=3, rotation=90, flipVertical=true\n- step 5: patternId=2, rotation=0, flipVertical=true\n- step 6: patternId=K, rotation=180, flipVertical=true\n- step 7: patternId=B, rotation=180, flipVertical=true\n- allowed patternId values for this task: O, 2, K, 3, B, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C209"} +{"sample_id": "C210", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> E -> E -> N -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "E", "E", "N", "N", "W"], "observed_path_faces": [{"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C210_path_sequence.png"}, "metadata": {"level_id": 210, "name": "Reconstruct 210", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-210.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["M", "B", "N", "triangle", "arrow_up", "3"], "start_x": 2, "start_y": 3, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "M", "rotation": 270}, "BOTTOM": {"patternId": "3", "rotation": 270}, "FRONT": {"patternId": "B", "rotation": 90}, "BACK": {"patternId": "triangle", "rotation": 180}, "LEFT": {"patternId": "arrow_up", "rotation": 180}, "RIGHT": {"patternId": "N", "rotation": 0}}, "bottom_faces": [{"patternId": "3", "rotation": 270, "x": 2, "y": 3}, {"patternId": "arrow_up", "rotation": 90, "x": 1, "y": 3}, {"patternId": "3", "rotation": 270, "x": 2, "y": 3}, {"patternId": "N", "rotation": 90, "x": 3, "y": 3}, {"patternId": "triangle", "rotation": 270, "x": 3, "y": 2}, {"patternId": "arrow_up", "rotation": 270, "x": 3, "y": 1}, {"patternId": "3", "rotation": 90, "x": 2, "y": 1}], "slot_sequence": ["LEFT", "BOTTOM", "RIGHT", "BACK", "LEFT", "BOTTOM"], "required_slots": ["LEFT", "BOTTOM", "RIGHT", "BACK"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "3", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "triangle", "rotation": 0}, "LEFT": {"patternId": "arrow_up", "rotation": 270}, "RIGHT": {"patternId": "N", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "3", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "triangle", "rotation": 0}, "LEFT": {"patternId": "arrow_up", "rotation": 270}, "RIGHT": {"patternId": "N", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C210\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): W -> E -> E -> N -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_up, rotation=90, flipVertical=true\n- step 2: patternId=3, rotation=270, flipVertical=true\n- step 3: patternId=N, rotation=90, flipVertical=true\n- step 4: patternId=triangle, rotation=270, flipVertical=true\n- step 5: patternId=arrow_up, rotation=270, flipVertical=true\n- step 6: patternId=3, rotation=90, flipVertical=true\n- allowed patternId values for this task: arrow_up, 3, N, triangle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C210"} +{"sample_id": "C211", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> W -> W -> N -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "W", "W", "N", "S"], "observed_path_faces": [{"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C211_path_sequence.png"}, "metadata": {"level_id": 211, "name": "Reconstruct 211", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-211.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["diamond", "8", "U", "1", "U", "6"], "start_x": 4, "start_y": 1, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "diamond", "rotation": 90}, "BOTTOM": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "8", "rotation": 0}, "BACK": {"patternId": "1", "rotation": 0}, "LEFT": {"patternId": "U", "rotation": 180}, "RIGHT": {"patternId": "U", "rotation": 90}}, "bottom_faces": [{"patternId": "6", "rotation": 180, "x": 4, "y": 1}, {"patternId": "8", "rotation": 0, "x": 4, "y": 2}, {"patternId": "U", "rotation": 180, "x": 3, "y": 2}, {"patternId": "1", "rotation": 0, "x": 2, "y": 2}, {"patternId": "U", "rotation": 90, "x": 1, "y": 2}, {"patternId": "6", "rotation": 90, "x": 1, "y": 1}, {"patternId": "U", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["FRONT", "LEFT", "BACK", "RIGHT", "BOTTOM", "RIGHT"], "required_slots": ["FRONT", "LEFT", "BACK", "RIGHT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "8", "rotation": 0}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "U", "rotation": 270}, "RIGHT": {"patternId": "U", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "8", "rotation": 0}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "U", "rotation": 270}, "RIGHT": {"patternId": "U", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C211\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> W -> W -> N -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=8, rotation=0, flipVertical=true\n- step 2: patternId=U, rotation=180, flipVertical=true\n- step 3: patternId=1, rotation=0, flipVertical=true\n- step 4: patternId=U, rotation=90, flipVertical=true\n- step 5: patternId=6, rotation=90, flipVertical=true\n- step 6: patternId=U, rotation=90, flipVertical=true\n- allowed patternId values for this task: 8, U, 1, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C211"} +{"sample_id": "C212", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> N -> W -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "N", "W", "N", "W"], "observed_path_faces": [{"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C212_path_sequence.png"}, "metadata": {"level_id": 212, "name": "Reconstruct 212", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-212.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["7", "W", "star", "I", "circle", "6"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "7", "rotation": 90}, "BOTTOM": {"patternId": "6", "rotation": 270}, "FRONT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "I", "rotation": 180}, "LEFT": {"patternId": "circle", "rotation": 270}, "RIGHT": {"patternId": "star", "rotation": 180}}, "bottom_faces": [{"patternId": "6", "rotation": 270, "x": 3, "y": 1}, {"patternId": "W", "rotation": 90, "x": 3, "y": 2}, {"patternId": "7", "rotation": 90, "x": 3, "y": 3}, {"patternId": "W", "rotation": 90, "x": 3, "y": 2}, {"patternId": "circle", "rotation": 270, "x": 2, "y": 2}, {"patternId": "6", "rotation": 0, "x": 2, "y": 1}, {"patternId": "I", "rotation": 90, "x": 1, "y": 1}], "slot_sequence": ["FRONT", "TOP", "FRONT", "LEFT", "BOTTOM", "BACK"], "required_slots": ["FRONT", "TOP", "LEFT", "BOTTOM", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "7", "rotation": 90}, "BOTTOM": {"patternId": "6", "rotation": 270}, "FRONT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "I", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "7", "rotation": 90}, "BOTTOM": {"patternId": "6", "rotation": 270}, "FRONT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "I", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C212\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> N -> W -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=W, rotation=90, flipVertical=true\n- step 2: patternId=7, rotation=90, flipVertical=true\n- step 3: patternId=W, rotation=90, flipVertical=true\n- step 4: patternId=circle, rotation=270, flipVertical=true\n- step 5: patternId=6, rotation=0, flipVertical=true\n- step 6: patternId=I, rotation=90, flipVertical=true\n- allowed patternId values for this task: W, 7, circle, 6, I, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C212"} +{"sample_id": "C213", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> S -> S -> E -> S -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "S", "S", "E", "S", "W", "S"], "observed_path_faces": [{"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C213_path_sequence.png"}, "metadata": {"level_id": 213, "name": "Reconstruct 213", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-213.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Y", "plus", "D", "V", "B", "B"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "Y", "rotation": 90}, "BOTTOM": {"patternId": "B", "rotation": 180}, "FRONT": {"patternId": "plus", "rotation": 180}, "BACK": {"patternId": "V", "rotation": 90}, "LEFT": {"patternId": "B", "rotation": 270}, "RIGHT": {"patternId": "D", "rotation": 270}}, "bottom_faces": [{"patternId": "B", "rotation": 180, "x": 1, "y": 2}, {"patternId": "V", "rotation": 270, "x": 1, "y": 1}, {"patternId": "B", "rotation": 180, "x": 1, "y": 2}, {"patternId": "plus", "rotation": 180, "x": 1, "y": 3}, {"patternId": "D", "rotation": 270, "x": 2, "y": 3}, {"patternId": "Y", "rotation": 180, "x": 2, "y": 4}, {"patternId": "plus", "rotation": 270, "x": 1, "y": 4}, {"patternId": "B", "rotation": 0, "x": 1, "y": 5}], "slot_sequence": ["BACK", "BOTTOM", "FRONT", "RIGHT", "TOP", "FRONT", "LEFT"], "required_slots": ["BACK", "BOTTOM", "FRONT", "RIGHT", "TOP", "LEFT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "Y", "rotation": 90}, "BOTTOM": {"patternId": "B", "rotation": 180}, "FRONT": {"patternId": "plus", "rotation": 180}, "BACK": {"patternId": "V", "rotation": 270}, "LEFT": {"patternId": "B", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "Y", "rotation": 90}, "BOTTOM": {"patternId": "B", "rotation": 180}, "FRONT": {"patternId": "plus", "rotation": 180}, "BACK": {"patternId": "V", "rotation": 270}, "LEFT": {"patternId": "B", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C213\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): N -> S -> S -> E -> S -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=V, rotation=270, flipVertical=true\n- step 2: patternId=B, rotation=180, flipVertical=true\n- step 3: patternId=plus, rotation=180, flipVertical=true\n- step 4: patternId=D, rotation=270, flipVertical=true\n- step 5: patternId=Y, rotation=180, flipVertical=true\n- step 6: patternId=plus, rotation=270, flipVertical=true\n- step 7: patternId=B, rotation=0, flipVertical=true\n- allowed patternId values for this task: V, B, plus, D, Y, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C213"} +{"sample_id": "C214", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> S -> N -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "S", "N", "E", "S"], "observed_path_faces": [{"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C214_path_sequence.png"}, "metadata": {"level_id": 214, "name": "Reconstruct 214", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-214.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_up", "8", "D", "Q", "Y", "V"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "arrow_up", "rotation": 180}, "BOTTOM": {"patternId": "V", "rotation": 270}, "FRONT": {"patternId": "8", "rotation": 90}, "BACK": {"patternId": "Q", "rotation": 180}, "LEFT": {"patternId": "Y", "rotation": 180}, "RIGHT": {"patternId": "D", "rotation": 90}}, "bottom_faces": [{"patternId": "V", "rotation": 270, "x": 1, "y": 1}, {"patternId": "D", "rotation": 180, "x": 2, "y": 1}, {"patternId": "8", "rotation": 180, "x": 2, "y": 2}, {"patternId": "Y", "rotation": 270, "x": 2, "y": 3}, {"patternId": "8", "rotation": 180, "x": 2, "y": 2}, {"patternId": "arrow_up", "rotation": 270, "x": 3, "y": 2}, {"patternId": "Y", "rotation": 0, "x": 3, "y": 3}], "slot_sequence": ["RIGHT", "FRONT", "LEFT", "FRONT", "TOP", "LEFT"], "required_slots": ["RIGHT", "FRONT", "LEFT", "TOP"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "arrow_up", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "8", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 270}, "RIGHT": {"patternId": "D", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "arrow_up", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "8", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 270}, "RIGHT": {"patternId": "D", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C214\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> S -> N -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=D, rotation=180, flipVertical=true\n- step 2: patternId=8, rotation=180, flipVertical=true\n- step 3: patternId=Y, rotation=270, flipVertical=true\n- step 4: patternId=8, rotation=180, flipVertical=true\n- step 5: patternId=arrow_up, rotation=270, flipVertical=true\n- step 6: patternId=Y, rotation=0, flipVertical=true\n- allowed patternId values for this task: D, 8, Y, arrow_up, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C214"} +{"sample_id": "C215", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> W -> S -> W -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "W", "S", "W", "S", "E"], "observed_path_faces": [{"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C215_path_sequence.png"}, "metadata": {"level_id": 215, "name": "Reconstruct 215", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-215.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["triangle", "arrow_up", "L", "K", "P", "circle"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "triangle", "rotation": 270}, "BOTTOM": {"patternId": "circle", "rotation": 180}, "FRONT": {"patternId": "arrow_up", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 90}, "LEFT": {"patternId": "P", "rotation": 0}, "RIGHT": {"patternId": "L", "rotation": 180}}, "bottom_faces": [{"patternId": "circle", "rotation": 180, "x": 3, "y": 1}, {"patternId": "arrow_up", "rotation": 0, "x": 3, "y": 2}, {"patternId": "triangle", "rotation": 270, "x": 3, "y": 3}, {"patternId": "P", "rotation": 90, "x": 2, "y": 3}, {"patternId": "K", "rotation": 180, "x": 2, "y": 4}, {"patternId": "circle", "rotation": 90, "x": 1, "y": 4}, {"patternId": "L", "rotation": 180, "x": 1, "y": 5}, {"patternId": "K", "rotation": 90, "x": 2, "y": 5}], "slot_sequence": ["FRONT", "TOP", "LEFT", "BACK", "BOTTOM", "RIGHT", "BACK"], "required_slots": ["FRONT", "TOP", "LEFT", "BACK", "BOTTOM", "RIGHT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "triangle", "rotation": 270}, "BOTTOM": {"patternId": "circle", "rotation": 180}, "FRONT": {"patternId": "arrow_up", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "P", "rotation": 90}, "RIGHT": {"patternId": "L", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "triangle", "rotation": 270}, "BOTTOM": {"patternId": "circle", "rotation": 180}, "FRONT": {"patternId": "arrow_up", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "P", "rotation": 90}, "RIGHT": {"patternId": "L", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C215\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> W -> S -> W -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_up, rotation=0, flipVertical=true\n- step 2: patternId=triangle, rotation=270, flipVertical=true\n- step 3: patternId=P, rotation=90, flipVertical=true\n- step 4: patternId=K, rotation=180, flipVertical=true\n- step 5: patternId=circle, rotation=90, flipVertical=true\n- step 6: patternId=L, rotation=180, flipVertical=true\n- step 7: patternId=K, rotation=90, flipVertical=true\n- allowed patternId values for this task: arrow_up, triangle, P, K, circle, L, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C215"} +{"sample_id": "C216", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> N -> E -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "N", "E", "N", "E"], "observed_path_faces": [{"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C216_path_sequence.png"}, "metadata": {"level_id": 216, "name": "Reconstruct 216", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-216.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["S", "S", "5", "circle", "Z", "E"], "start_x": 1, "start_y": 3, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "S", "rotation": 180}, "BOTTOM": {"patternId": "E", "rotation": 0}, "FRONT": {"patternId": "S", "rotation": 90}, "BACK": {"patternId": "circle", "rotation": 90}, "LEFT": {"patternId": "Z", "rotation": 270}, "RIGHT": {"patternId": "5", "rotation": 270}}, "bottom_faces": [{"patternId": "E", "rotation": 0, "x": 1, "y": 3}, {"patternId": "5", "rotation": 0, "x": 2, "y": 3}, {"patternId": "S", "rotation": 0, "x": 3, "y": 3}, {"patternId": "circle", "rotation": 90, "x": 3, "y": 2}, {"patternId": "Z", "rotation": 270, "x": 4, "y": 2}, {"patternId": "E", "rotation": 90, "x": 4, "y": 1}, {"patternId": "S", "rotation": 180, "x": 5, "y": 1}], "slot_sequence": ["RIGHT", "TOP", "BACK", "LEFT", "BOTTOM", "FRONT"], "required_slots": ["RIGHT", "TOP", "BACK", "LEFT", "BOTTOM", "FRONT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "S", "rotation": 180}, "BOTTOM": {"patternId": "E", "rotation": 0}, "FRONT": {"patternId": "S", "rotation": 90}, "BACK": {"patternId": "circle", "rotation": 270}, "LEFT": {"patternId": "Z", "rotation": 0}, "RIGHT": {"patternId": "5", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 180}, "BOTTOM": {"patternId": "E", "rotation": 0}, "FRONT": {"patternId": "S", "rotation": 90}, "BACK": {"patternId": "circle", "rotation": 270}, "LEFT": {"patternId": "Z", "rotation": 0}, "RIGHT": {"patternId": "5", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C216\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> N -> E -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=5, rotation=0, flipVertical=true\n- step 2: patternId=S, rotation=0, flipVertical=true\n- step 3: patternId=circle, rotation=90, flipVertical=true\n- step 4: patternId=Z, rotation=270, flipVertical=true\n- step 5: patternId=E, rotation=90, flipVertical=true\n- step 6: patternId=S, rotation=180, flipVertical=true\n- allowed patternId values for this task: 5, S, circle, Z, E, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C216"} +{"sample_id": "C217", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> E -> S -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "W", "E", "S", "W", "W"], "observed_path_faces": [{"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C217_path_sequence.png"}, "metadata": {"level_id": 217, "name": "Reconstruct 217", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-217.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["M", "square", "square", "I", "star", "I"], "start_x": 2, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "M", "rotation": 0}, "BOTTOM": {"patternId": "I", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 270}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "star", "rotation": 180}, "RIGHT": {"patternId": "square", "rotation": 0}}, "bottom_faces": [{"patternId": "I", "rotation": 0, "x": 2, "y": 1}, {"patternId": "square", "rotation": 90, "x": 3, "y": 1}, {"patternId": "square", "rotation": 0, "x": 3, "y": 2}, {"patternId": "I", "rotation": 90, "x": 2, "y": 2}, {"patternId": "square", "rotation": 0, "x": 3, "y": 2}, {"patternId": "star", "rotation": 270, "x": 3, "y": 3}, {"patternId": "I", "rotation": 180, "x": 2, "y": 3}, {"patternId": "square", "rotation": 270, "x": 1, "y": 3}], "slot_sequence": ["RIGHT", "FRONT", "BOTTOM", "FRONT", "LEFT", "BOTTOM", "RIGHT"], "required_slots": ["RIGHT", "FRONT", "BOTTOM", "LEFT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "I", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 270}, "RIGHT": {"patternId": "square", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "I", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 270}, "RIGHT": {"patternId": "square", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C217\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> E -> S -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=square, rotation=90, flipVertical=true\n- step 2: patternId=square, rotation=0, flipVertical=true\n- step 3: patternId=I, rotation=90, flipVertical=true\n- step 4: patternId=square, rotation=0, flipVertical=true\n- step 5: patternId=star, rotation=270, flipVertical=true\n- step 6: patternId=I, rotation=180, flipVertical=true\n- step 7: patternId=square, rotation=270, flipVertical=true\n- allowed patternId values for this task: square, I, star, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C217"} +{"sample_id": "C218", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> S -> E -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "S", "E", "N", "N"], "observed_path_faces": [{"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C218_path_sequence.png"}, "metadata": {"level_id": 218, "name": "Reconstruct 218", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-218.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["K", "Z", "Z", "K", "Y", "G"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "K", "rotation": 270}, "BOTTOM": {"patternId": "G", "rotation": 180}, "FRONT": {"patternId": "Z", "rotation": 180}, "BACK": {"patternId": "K", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 180}, "RIGHT": {"patternId": "Z", "rotation": 90}}, "bottom_faces": [{"patternId": "G", "rotation": 180, "x": 2, "y": 1}, {"patternId": "Y", "rotation": 90, "x": 1, "y": 1}, {"patternId": "Z", "rotation": 90, "x": 1, "y": 2}, {"patternId": "Z", "rotation": 0, "x": 1, "y": 3}, {"patternId": "G", "rotation": 0, "x": 2, "y": 3}, {"patternId": "Z", "rotation": 0, "x": 2, "y": 2}, {"patternId": "K", "rotation": 90, "x": 2, "y": 1}], "slot_sequence": ["LEFT", "FRONT", "RIGHT", "BOTTOM", "FRONT", "TOP"], "required_slots": ["LEFT", "FRONT", "RIGHT", "BOTTOM", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "K", "rotation": 270}, "BOTTOM": {"patternId": "G", "rotation": 180}, "FRONT": {"patternId": "Z", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 270}, "RIGHT": {"patternId": "Z", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "K", "rotation": 270}, "BOTTOM": {"patternId": "G", "rotation": 180}, "FRONT": {"patternId": "Z", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 270}, "RIGHT": {"patternId": "Z", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C218\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> S -> E -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Y, rotation=90, flipVertical=true\n- step 2: patternId=Z, rotation=90, flipVertical=true\n- step 3: patternId=Z, rotation=0, flipVertical=true\n- step 4: patternId=G, rotation=0, flipVertical=true\n- step 5: patternId=Z, rotation=0, flipVertical=true\n- step 6: patternId=K, rotation=90, flipVertical=true\n- allowed patternId values for this task: Y, Z, G, K, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C218"} +{"sample_id": "C219", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> E -> N -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "E", "N", "S", "S"], "observed_path_faces": [{"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C219_path_sequence.png"}, "metadata": {"level_id": 219, "name": "Reconstruct 219", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-219.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["7", "triangle", "S", "W", "D", "A"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "7", "rotation": 270}, "BOTTOM": {"patternId": "A", "rotation": 0}, "FRONT": {"patternId": "triangle", "rotation": 90}, "BACK": {"patternId": "W", "rotation": 270}, "LEFT": {"patternId": "D", "rotation": 270}, "RIGHT": {"patternId": "S", "rotation": 270}}, "bottom_faces": [{"patternId": "A", "rotation": 0, "x": 2, "y": 1}, {"patternId": "triangle", "rotation": 90, "x": 2, "y": 2}, {"patternId": "D", "rotation": 270, "x": 1, "y": 2}, {"patternId": "triangle", "rotation": 90, "x": 2, "y": 2}, {"patternId": "A", "rotation": 0, "x": 2, "y": 1}, {"patternId": "triangle", "rotation": 90, "x": 2, "y": 2}, {"patternId": "7", "rotation": 270, "x": 2, "y": 3}], "slot_sequence": ["FRONT", "LEFT", "FRONT", "BOTTOM", "FRONT", "TOP"], "required_slots": ["FRONT", "LEFT", "BOTTOM", "TOP"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "7", "rotation": 270}, "BOTTOM": {"patternId": "A", "rotation": 0}, "FRONT": {"patternId": "triangle", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "7", "rotation": 270}, "BOTTOM": {"patternId": "A", "rotation": 0}, "FRONT": {"patternId": "triangle", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C219\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> E -> N -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=triangle, rotation=90, flipVertical=true\n- step 2: patternId=D, rotation=270, flipVertical=true\n- step 3: patternId=triangle, rotation=90, flipVertical=true\n- step 4: patternId=A, rotation=0, flipVertical=true\n- step 5: patternId=triangle, rotation=90, flipVertical=true\n- step 6: patternId=7, rotation=270, flipVertical=true\n- allowed patternId values for this task: triangle, D, A, 7, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C219"} +{"sample_id": "C220", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> S -> S -> E -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "S", "S", "E", "N", "W"], "observed_path_faces": [{"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C220_path_sequence.png"}, "metadata": {"level_id": 220, "name": "Reconstruct 220", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-220.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["E", "L", "Z", "M", "3", "G"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "E", "rotation": 180}, "BOTTOM": {"patternId": "G", "rotation": 180}, "FRONT": {"patternId": "L", "rotation": 180}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "3", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 0}}, "bottom_faces": [{"patternId": "G", "rotation": 180, "x": 1, "y": 2}, {"patternId": "M", "rotation": 270, "x": 1, "y": 1}, {"patternId": "G", "rotation": 180, "x": 1, "y": 2}, {"patternId": "L", "rotation": 180, "x": 1, "y": 3}, {"patternId": "Z", "rotation": 0, "x": 2, "y": 3}, {"patternId": "G", "rotation": 90, "x": 2, "y": 2}, {"patternId": "L", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["BACK", "BOTTOM", "FRONT", "RIGHT", "BOTTOM", "FRONT"], "required_slots": ["BACK", "BOTTOM", "FRONT", "RIGHT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "G", "rotation": 180}, "FRONT": {"patternId": "L", "rotation": 180}, "BACK": {"patternId": "M", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "G", "rotation": 180}, "FRONT": {"patternId": "L", "rotation": 180}, "BACK": {"patternId": "M", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C220\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): N -> S -> S -> E -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=M, rotation=270, flipVertical=true\n- step 2: patternId=G, rotation=180, flipVertical=true\n- step 3: patternId=L, rotation=180, flipVertical=true\n- step 4: patternId=Z, rotation=0, flipVertical=true\n- step 5: patternId=G, rotation=90, flipVertical=true\n- step 6: patternId=L, rotation=90, flipVertical=true\n- allowed patternId values for this task: M, G, L, Z, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C220"} +{"sample_id": "C221", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> N -> E -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "N", "E", "N", "N"], "observed_path_faces": [{"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C221_path_sequence.png"}, "metadata": {"level_id": 221, "name": "Reconstruct 221", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-221.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["plus", "square", "E", "triangle", "4", "1"], "start_x": 2, "start_y": 5, "grid_width": 4, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "plus", "rotation": 270}, "BOTTOM": {"patternId": "1", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 180}, "BACK": {"patternId": "triangle", "rotation": 180}, "LEFT": {"patternId": "4", "rotation": 90}, "RIGHT": {"patternId": "E", "rotation": 0}}, "bottom_faces": [{"patternId": "1", "rotation": 0, "x": 2, "y": 5}, {"patternId": "4", "rotation": 0, "x": 1, "y": 5}, {"patternId": "triangle", "rotation": 90, "x": 1, "y": 4}, {"patternId": "E", "rotation": 270, "x": 1, "y": 3}, {"patternId": "1", "rotation": 180, "x": 2, "y": 3}, {"patternId": "square", "rotation": 0, "x": 2, "y": 2}, {"patternId": "plus", "rotation": 90, "x": 2, "y": 1}], "slot_sequence": ["LEFT", "BACK", "RIGHT", "BOTTOM", "FRONT", "TOP"], "required_slots": ["LEFT", "BACK", "RIGHT", "BOTTOM", "FRONT", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "plus", "rotation": 270}, "BOTTOM": {"patternId": "1", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 180}, "BACK": {"patternId": "triangle", "rotation": 0}, "LEFT": {"patternId": "4", "rotation": 180}, "RIGHT": {"patternId": "E", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "plus", "rotation": 270}, "BOTTOM": {"patternId": "1", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 180}, "BACK": {"patternId": "triangle", "rotation": 0}, "LEFT": {"patternId": "4", "rotation": 180}, "RIGHT": {"patternId": "E", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C221\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> N -> E -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=4, rotation=0, flipVertical=true\n- step 2: patternId=triangle, rotation=90, flipVertical=true\n- step 3: patternId=E, rotation=270, flipVertical=true\n- step 4: patternId=1, rotation=180, flipVertical=true\n- step 5: patternId=square, rotation=0, flipVertical=true\n- step 6: patternId=plus, rotation=90, flipVertical=true\n- allowed patternId values for this task: 4, triangle, E, 1, square, plus, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C221"} +{"sample_id": "C222", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> N -> W -> S -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "N", "W", "S", "W", "W"], "observed_path_faces": [{"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C222_path_sequence.png"}, "metadata": {"level_id": 222, "name": "Reconstruct 222", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-222.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["C", "star", "H", "T", "7", "S"], "start_x": 6, "start_y": 2, "grid_width": 8, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "C", "rotation": 270}, "BOTTOM": {"patternId": "S", "rotation": 180}, "FRONT": {"patternId": "star", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 270}, "LEFT": {"patternId": "7", "rotation": 180}, "RIGHT": {"patternId": "H", "rotation": 270}}, "bottom_faces": [{"patternId": "S", "rotation": 180, "x": 6, "y": 2}, {"patternId": "7", "rotation": 90, "x": 5, "y": 2}, {"patternId": "C", "rotation": 90, "x": 4, "y": 2}, {"patternId": "T", "rotation": 270, "x": 4, "y": 1}, {"patternId": "H", "rotation": 270, "x": 3, "y": 1}, {"patternId": "C", "rotation": 0, "x": 3, "y": 2}, {"patternId": "star", "rotation": 90, "x": 2, "y": 2}, {"patternId": "S", "rotation": 270, "x": 1, "y": 2}], "slot_sequence": ["LEFT", "TOP", "BACK", "RIGHT", "TOP", "FRONT", "BOTTOM"], "required_slots": ["LEFT", "TOP", "BACK", "RIGHT", "FRONT", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "C", "rotation": 270}, "BOTTOM": {"patternId": "S", "rotation": 180}, "FRONT": {"patternId": "star", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 90}, "LEFT": {"patternId": "7", "rotation": 270}, "RIGHT": {"patternId": "H", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "C", "rotation": 270}, "BOTTOM": {"patternId": "S", "rotation": 180}, "FRONT": {"patternId": "star", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 90}, "LEFT": {"patternId": "7", "rotation": 270}, "RIGHT": {"patternId": "H", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C222\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> N -> W -> S -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=7, rotation=90, flipVertical=true\n- step 2: patternId=C, rotation=90, flipVertical=true\n- step 3: patternId=T, rotation=270, flipVertical=true\n- step 4: patternId=H, rotation=270, flipVertical=true\n- step 5: patternId=C, rotation=0, flipVertical=true\n- step 6: patternId=star, rotation=90, flipVertical=true\n- step 7: patternId=S, rotation=270, flipVertical=true\n- allowed patternId values for this task: 7, C, T, H, star, S, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C222"} +{"sample_id": "C223", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> N -> E -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "N", "E", "W", "S"], "observed_path_faces": [{"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C223_path_sequence.png"}, "metadata": {"level_id": 223, "name": "Reconstruct 223", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-223.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["C", "I", "G", "I", "1", "Z"], "start_x": 1, "start_y": 2, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "C", "rotation": 270}, "BOTTOM": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "I", "rotation": 90}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "1", "rotation": 270}, "RIGHT": {"patternId": "G", "rotation": 180}}, "bottom_faces": [{"patternId": "Z", "rotation": 270, "x": 1, "y": 2}, {"patternId": "G", "rotation": 270, "x": 2, "y": 2}, {"patternId": "C", "rotation": 90, "x": 3, "y": 2}, {"patternId": "I", "rotation": 270, "x": 3, "y": 1}, {"patternId": "1", "rotation": 270, "x": 4, "y": 1}, {"patternId": "I", "rotation": 270, "x": 3, "y": 1}, {"patternId": "C", "rotation": 90, "x": 3, "y": 2}], "slot_sequence": ["RIGHT", "TOP", "BACK", "LEFT", "BACK", "TOP"], "required_slots": ["RIGHT", "TOP", "BACK", "LEFT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "C", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 0}, "RIGHT": {"patternId": "G", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "C", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 0}, "RIGHT": {"patternId": "G", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C223\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> N -> E -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=G, rotation=270, flipVertical=true\n- step 2: patternId=C, rotation=90, flipVertical=true\n- step 3: patternId=I, rotation=270, flipVertical=true\n- step 4: patternId=1, rotation=270, flipVertical=true\n- step 5: patternId=I, rotation=270, flipVertical=true\n- step 6: patternId=C, rotation=90, flipVertical=true\n- allowed patternId values for this task: G, C, I, 1, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C223"} +{"sample_id": "C224", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> S -> E -> E -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "S", "E", "E", "W"], "observed_path_faces": [{"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C224_path_sequence.png"}, "metadata": {"level_id": 224, "name": "Reconstruct 224", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-224.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["smile", "square", "4", "D", "circle", "triangle"], "start_x": 1, "start_y": 2, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "smile", "rotation": 0}, "BOTTOM": {"patternId": "triangle", "rotation": 90}, "FRONT": {"patternId": "square", "rotation": 180}, "BACK": {"patternId": "D", "rotation": 180}, "LEFT": {"patternId": "circle", "rotation": 90}, "RIGHT": {"patternId": "4", "rotation": 270}}, "bottom_faces": [{"patternId": "triangle", "rotation": 90, "x": 1, "y": 2}, {"patternId": "D", "rotation": 0, "x": 1, "y": 1}, {"patternId": "4", "rotation": 90, "x": 2, "y": 1}, {"patternId": "triangle", "rotation": 180, "x": 2, "y": 2}, {"patternId": "square", "rotation": 270, "x": 3, "y": 2}, {"patternId": "smile", "rotation": 90, "x": 4, "y": 2}, {"patternId": "square", "rotation": 270, "x": 3, "y": 2}], "slot_sequence": ["BACK", "RIGHT", "BOTTOM", "FRONT", "TOP", "FRONT"], "required_slots": ["BACK", "RIGHT", "BOTTOM", "FRONT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "smile", "rotation": 0}, "BOTTOM": {"patternId": "triangle", "rotation": 90}, "FRONT": {"patternId": "square", "rotation": 180}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "4", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 0}, "BOTTOM": {"patternId": "triangle", "rotation": 90}, "FRONT": {"patternId": "square", "rotation": 180}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "4", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C224\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> S -> E -> E -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=D, rotation=0, flipVertical=true\n- step 2: patternId=4, rotation=90, flipVertical=true\n- step 3: patternId=triangle, rotation=180, flipVertical=true\n- step 4: patternId=square, rotation=270, flipVertical=true\n- step 5: patternId=smile, rotation=90, flipVertical=true\n- step 6: patternId=square, rotation=270, flipVertical=true\n- allowed patternId values for this task: D, 4, triangle, square, smile, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C224"} +{"sample_id": "C225", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> N -> E -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "N", "E", "N", "N"], "observed_path_faces": [{"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C225_path_sequence.png"}, "metadata": {"level_id": 225, "name": "Reconstruct 225", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-225.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Z", "B", "smile", "H", "U", "O"], "start_x": 1, "start_y": 5, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "Z", "rotation": 90}, "BOTTOM": {"patternId": "O", "rotation": 180}, "FRONT": {"patternId": "B", "rotation": 180}, "BACK": {"patternId": "H", "rotation": 90}, "LEFT": {"patternId": "U", "rotation": 0}, "RIGHT": {"patternId": "smile", "rotation": 90}}, "bottom_faces": [{"patternId": "O", "rotation": 180, "x": 1, "y": 5}, {"patternId": "smile", "rotation": 180, "x": 2, "y": 5}, {"patternId": "H", "rotation": 180, "x": 2, "y": 4}, {"patternId": "U", "rotation": 90, "x": 2, "y": 3}, {"patternId": "Z", "rotation": 90, "x": 3, "y": 3}, {"patternId": "B", "rotation": 180, "x": 3, "y": 2}, {"patternId": "O", "rotation": 180, "x": 3, "y": 1}], "slot_sequence": ["RIGHT", "BACK", "LEFT", "TOP", "FRONT", "BOTTOM"], "required_slots": ["RIGHT", "BACK", "LEFT", "TOP", "FRONT", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "Z", "rotation": 90}, "BOTTOM": {"patternId": "O", "rotation": 180}, "FRONT": {"patternId": "B", "rotation": 180}, "BACK": {"patternId": "H", "rotation": 270}, "LEFT": {"patternId": "U", "rotation": 90}, "RIGHT": {"patternId": "smile", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "Z", "rotation": 90}, "BOTTOM": {"patternId": "O", "rotation": 180}, "FRONT": {"patternId": "B", "rotation": 180}, "BACK": {"patternId": "H", "rotation": 270}, "LEFT": {"patternId": "U", "rotation": 90}, "RIGHT": {"patternId": "smile", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C225\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> N -> E -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=smile, rotation=180, flipVertical=true\n- step 2: patternId=H, rotation=180, flipVertical=true\n- step 3: patternId=U, rotation=90, flipVertical=true\n- step 4: patternId=Z, rotation=90, flipVertical=true\n- step 5: patternId=B, rotation=180, flipVertical=true\n- step 6: patternId=O, rotation=180, flipVertical=true\n- allowed patternId values for this task: smile, H, U, Z, B, O, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C225"} +{"sample_id": "C226", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> E -> N -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "E", "N", "S", "E"], "observed_path_faces": [{"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C226_path_sequence.png"}, "metadata": {"level_id": 226, "name": "Reconstruct 226", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-226.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["star", "6", "2", "arrow_down", "B", "3"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "star", "rotation": 90}, "BOTTOM": {"patternId": "3", "rotation": 180}, "FRONT": {"patternId": "6", "rotation": 180}, "BACK": {"patternId": "arrow_down", "rotation": 0}, "LEFT": {"patternId": "B", "rotation": 270}, "RIGHT": {"patternId": "2", "rotation": 180}}, "bottom_faces": [{"patternId": "3", "rotation": 180, "x": 1, "y": 1}, {"patternId": "6", "rotation": 180, "x": 1, "y": 2}, {"patternId": "star", "rotation": 90, "x": 1, "y": 3}, {"patternId": "2", "rotation": 90, "x": 2, "y": 3}, {"patternId": "6", "rotation": 90, "x": 2, "y": 2}, {"patternId": "2", "rotation": 90, "x": 2, "y": 3}, {"patternId": "3", "rotation": 0, "x": 3, "y": 3}], "slot_sequence": ["FRONT", "TOP", "RIGHT", "FRONT", "RIGHT", "BOTTOM"], "required_slots": ["FRONT", "TOP", "RIGHT", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "star", "rotation": 90}, "BOTTOM": {"patternId": "3", "rotation": 180}, "FRONT": {"patternId": "6", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "2", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 90}, "BOTTOM": {"patternId": "3", "rotation": 180}, "FRONT": {"patternId": "6", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "2", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C226\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> E -> N -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=6, rotation=180, flipVertical=true\n- step 2: patternId=star, rotation=90, flipVertical=true\n- step 3: patternId=2, rotation=90, flipVertical=true\n- step 4: patternId=6, rotation=90, flipVertical=true\n- step 5: patternId=2, rotation=90, flipVertical=true\n- step 6: patternId=3, rotation=0, flipVertical=true\n- allowed patternId values for this task: 6, star, 2, 3, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C226"} +{"sample_id": "C227", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> N -> W -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "N", "W", "E", "N"], "observed_path_faces": [{"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C227_path_sequence.png"}, "metadata": {"level_id": 227, "name": "Reconstruct 227", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-227.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_up", "2", "4", "6", "C", "C"], "start_x": 3, "start_y": 2, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "arrow_up", "rotation": 270}, "BOTTOM": {"patternId": "C", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 90}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "C", "rotation": 180}, "RIGHT": {"patternId": "4", "rotation": 90}}, "bottom_faces": [{"patternId": "C", "rotation": 0, "x": 3, "y": 2}, {"patternId": "2", "rotation": 90, "x": 3, "y": 3}, {"patternId": "C", "rotation": 180, "x": 2, "y": 3}, {"patternId": "C", "rotation": 90, "x": 2, "y": 2}, {"patternId": "6", "rotation": 270, "x": 1, "y": 2}, {"patternId": "C", "rotation": 90, "x": 2, "y": 2}, {"patternId": "4", "rotation": 270, "x": 2, "y": 1}], "slot_sequence": ["FRONT", "LEFT", "BOTTOM", "BACK", "BOTTOM", "RIGHT"], "required_slots": ["FRONT", "LEFT", "BOTTOM", "BACK", "RIGHT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "C", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 90}, "BACK": {"patternId": "6", "rotation": 180}, "LEFT": {"patternId": "C", "rotation": 270}, "RIGHT": {"patternId": "4", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "C", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 90}, "BACK": {"patternId": "6", "rotation": 180}, "LEFT": {"patternId": "C", "rotation": 270}, "RIGHT": {"patternId": "4", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C227\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> N -> W -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=2, rotation=90, flipVertical=true\n- step 2: patternId=C, rotation=180, flipVertical=true\n- step 3: patternId=C, rotation=90, flipVertical=true\n- step 4: patternId=6, rotation=270, flipVertical=true\n- step 5: patternId=C, rotation=90, flipVertical=true\n- step 6: patternId=4, rotation=270, flipVertical=true\n- allowed patternId values for this task: 2, C, 6, 4, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C227"} +{"sample_id": "C228", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> N -> W -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "N", "W", "N", "W"], "observed_path_faces": [{"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C228_path_sequence.png"}, "metadata": {"level_id": 228, "name": "Reconstruct 228", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-228.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["star", "Q", "triangle", "2", "3", "8"], "start_x": 5, "start_y": 3, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "star", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "Q", "rotation": 270}, "BACK": {"patternId": "2", "rotation": 90}, "LEFT": {"patternId": "3", "rotation": 0}, "RIGHT": {"patternId": "triangle", "rotation": 0}}, "bottom_faces": [{"patternId": "8", "rotation": 180, "x": 5, "y": 3}, {"patternId": "3", "rotation": 270, "x": 4, "y": 3}, {"patternId": "star", "rotation": 180, "x": 3, "y": 3}, {"patternId": "2", "rotation": 90, "x": 3, "y": 2}, {"patternId": "triangle", "rotation": 0, "x": 2, "y": 2}, {"patternId": "8", "rotation": 90, "x": 2, "y": 1}, {"patternId": "Q", "rotation": 180, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "TOP", "BACK", "RIGHT", "BOTTOM", "FRONT"], "required_slots": ["LEFT", "TOP", "BACK", "RIGHT", "BOTTOM", "FRONT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "star", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "Q", "rotation": 270}, "BACK": {"patternId": "2", "rotation": 270}, "LEFT": {"patternId": "3", "rotation": 90}, "RIGHT": {"patternId": "triangle", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "Q", "rotation": 270}, "BACK": {"patternId": "2", "rotation": 270}, "LEFT": {"patternId": "3", "rotation": 90}, "RIGHT": {"patternId": "triangle", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C228\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> N -> W -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=3, rotation=270, flipVertical=true\n- step 2: patternId=star, rotation=180, flipVertical=true\n- step 3: patternId=2, rotation=90, flipVertical=true\n- step 4: patternId=triangle, rotation=0, flipVertical=true\n- step 5: patternId=8, rotation=90, flipVertical=true\n- step 6: patternId=Q, rotation=180, flipVertical=true\n- allowed patternId values for this task: 3, star, 2, triangle, 8, Q, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C228"} +{"sample_id": "C229", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> W -> N -> E -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "W", "N", "E", "N", "E"], "observed_path_faces": [{"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C229_path_sequence.png"}, "metadata": {"level_id": 229, "name": "Reconstruct 229", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-229.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Q", "9", "triangle", "I", "square", "R"], "start_x": 1, "start_y": 3, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "Q", "rotation": 270}, "BOTTOM": {"patternId": "R", "rotation": 270}, "FRONT": {"patternId": "9", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 180}, "LEFT": {"patternId": "square", "rotation": 180}, "RIGHT": {"patternId": "triangle", "rotation": 270}}, "bottom_faces": [{"patternId": "R", "rotation": 270, "x": 1, "y": 3}, {"patternId": "triangle", "rotation": 0, "x": 2, "y": 3}, {"patternId": "R", "rotation": 270, "x": 1, "y": 3}, {"patternId": "I", "rotation": 0, "x": 1, "y": 2}, {"patternId": "triangle", "rotation": 90, "x": 2, "y": 2}, {"patternId": "Q", "rotation": 180, "x": 2, "y": 1}, {"patternId": "9", "rotation": 270, "x": 3, "y": 1}], "slot_sequence": ["RIGHT", "BOTTOM", "BACK", "RIGHT", "TOP", "FRONT"], "required_slots": ["RIGHT", "BOTTOM", "BACK", "TOP", "FRONT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "Q", "rotation": 270}, "BOTTOM": {"patternId": "R", "rotation": 270}, "FRONT": {"patternId": "9", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "triangle", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "Q", "rotation": 270}, "BOTTOM": {"patternId": "R", "rotation": 270}, "FRONT": {"patternId": "9", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "triangle", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C229\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): E -> W -> N -> E -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=triangle, rotation=0, flipVertical=true\n- step 2: patternId=R, rotation=270, flipVertical=true\n- step 3: patternId=I, rotation=0, flipVertical=true\n- step 4: patternId=triangle, rotation=90, flipVertical=true\n- step 5: patternId=Q, rotation=180, flipVertical=true\n- step 6: patternId=9, rotation=270, flipVertical=true\n- allowed patternId values for this task: triangle, R, I, Q, 9, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C229"} +{"sample_id": "C230", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> W -> W -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "W", "W", "W", "S"], "observed_path_faces": [{"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C230_path_sequence.png"}, "metadata": {"level_id": 230, "name": "Reconstruct 230", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-230.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["P", "J", "2", "7", "W", "star"], "start_x": 3, "start_y": 2, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "P", "rotation": 270}, "BOTTOM": {"patternId": "star", "rotation": 90}, "FRONT": {"patternId": "J", "rotation": 270}, "BACK": {"patternId": "7", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "2", "rotation": 0}}, "bottom_faces": [{"patternId": "star", "rotation": 90, "x": 3, "y": 2}, {"patternId": "7", "rotation": 180, "x": 3, "y": 1}, {"patternId": "2", "rotation": 180, "x": 4, "y": 1}, {"patternId": "7", "rotation": 180, "x": 3, "y": 1}, {"patternId": "W", "rotation": 270, "x": 2, "y": 1}, {"patternId": "J", "rotation": 90, "x": 1, "y": 1}, {"patternId": "star", "rotation": 270, "x": 1, "y": 2}], "slot_sequence": ["BACK", "RIGHT", "BACK", "LEFT", "FRONT", "BOTTOM"], "required_slots": ["BACK", "RIGHT", "LEFT", "FRONT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "star", "rotation": 90}, "FRONT": {"patternId": "J", "rotation": 270}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "W", "rotation": 180}, "RIGHT": {"patternId": "2", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "star", "rotation": 90}, "FRONT": {"patternId": "J", "rotation": 270}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "W", "rotation": 180}, "RIGHT": {"patternId": "2", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C230\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> W -> W -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=7, rotation=180, flipVertical=true\n- step 2: patternId=2, rotation=180, flipVertical=true\n- step 3: patternId=7, rotation=180, flipVertical=true\n- step 4: patternId=W, rotation=270, flipVertical=true\n- step 5: patternId=J, rotation=90, flipVertical=true\n- step 6: patternId=star, rotation=270, flipVertical=true\n- allowed patternId values for this task: 7, 2, W, J, star, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C230"} +{"sample_id": "C231", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> S -> S -> E -> S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "S", "S", "E", "S", "N"], "observed_path_faces": [{"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C231_path_sequence.png"}, "metadata": {"level_id": 231, "name": "Reconstruct 231", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-231.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["1", "heart", "O", "L", "F", "D"], "start_x": 1, "start_y": 3, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "1", "rotation": 0}, "BOTTOM": {"patternId": "D", "rotation": 180}, "FRONT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "L", "rotation": 270}, "LEFT": {"patternId": "F", "rotation": 180}, "RIGHT": {"patternId": "O", "rotation": 90}}, "bottom_faces": [{"patternId": "D", "rotation": 180, "x": 1, "y": 3}, {"patternId": "L", "rotation": 90, "x": 1, "y": 2}, {"patternId": "1", "rotation": 0, "x": 1, "y": 1}, {"patternId": "L", "rotation": 90, "x": 1, "y": 2}, {"patternId": "D", "rotation": 180, "x": 1, "y": 3}, {"patternId": "O", "rotation": 180, "x": 2, "y": 3}, {"patternId": "heart", "rotation": 0, "x": 2, "y": 4}, {"patternId": "O", "rotation": 180, "x": 2, "y": 3}], "slot_sequence": ["BACK", "TOP", "BACK", "BOTTOM", "RIGHT", "FRONT", "RIGHT"], "required_slots": ["BACK", "TOP", "BOTTOM", "RIGHT", "FRONT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "1", "rotation": 0}, "BOTTOM": {"patternId": "D", "rotation": 180}, "FRONT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "L", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "1", "rotation": 0}, "BOTTOM": {"patternId": "D", "rotation": 180}, "FRONT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "L", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C231\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> S -> S -> E -> S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=L, rotation=90, flipVertical=true\n- step 2: patternId=1, rotation=0, flipVertical=true\n- step 3: patternId=L, rotation=90, flipVertical=true\n- step 4: patternId=D, rotation=180, flipVertical=true\n- step 5: patternId=O, rotation=180, flipVertical=true\n- step 6: patternId=heart, rotation=0, flipVertical=true\n- step 7: patternId=O, rotation=180, flipVertical=true\n- allowed patternId values for this task: L, 1, D, O, heart, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C231"} +{"sample_id": "C232", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> E -> S -> E -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "E", "S", "E", "N", "N"], "observed_path_faces": [{"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C232_path_sequence.png"}, "metadata": {"level_id": 232, "name": "Reconstruct 232", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-232.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["triangle", "4", "plus", "heart", "F", "heart"], "start_x": 1, "start_y": 1, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "triangle", "rotation": 270}, "BOTTOM": {"patternId": "heart", "rotation": 0}, "FRONT": {"patternId": "4", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 90}, "LEFT": {"patternId": "F", "rotation": 180}, "RIGHT": {"patternId": "plus", "rotation": 270}}, "bottom_faces": [{"patternId": "heart", "rotation": 0, "x": 1, "y": 1}, {"patternId": "4", "rotation": 0, "x": 1, "y": 2}, {"patternId": "plus", "rotation": 270, "x": 2, "y": 2}, {"patternId": "heart", "rotation": 90, "x": 3, "y": 2}, {"patternId": "triangle", "rotation": 90, "x": 3, "y": 3}, {"patternId": "F", "rotation": 90, "x": 4, "y": 3}, {"patternId": "heart", "rotation": 0, "x": 4, "y": 2}, {"patternId": "plus", "rotation": 180, "x": 4, "y": 1}], "slot_sequence": ["FRONT", "RIGHT", "BACK", "TOP", "LEFT", "BACK", "RIGHT"], "required_slots": ["FRONT", "RIGHT", "BACK", "TOP", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "triangle", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "4", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 270}, "LEFT": {"patternId": "F", "rotation": 270}, "RIGHT": {"patternId": "plus", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "triangle", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "4", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 270}, "LEFT": {"patternId": "F", "rotation": 270}, "RIGHT": {"patternId": "plus", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C232\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> E -> S -> E -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=4, rotation=0, flipVertical=true\n- step 2: patternId=plus, rotation=270, flipVertical=true\n- step 3: patternId=heart, rotation=90, flipVertical=true\n- step 4: patternId=triangle, rotation=90, flipVertical=true\n- step 5: patternId=F, rotation=90, flipVertical=true\n- step 6: patternId=heart, rotation=0, flipVertical=true\n- step 7: patternId=plus, rotation=180, flipVertical=true\n- allowed patternId values for this task: 4, plus, heart, triangle, F, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C232"} +{"sample_id": "C233", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> N -> W -> N -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "N", "W", "N", "W", "W"], "observed_path_faces": [{"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C233_path_sequence.png"}, "metadata": {"level_id": 233, "name": "Reconstruct 233", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-233.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["square", "E", "P", "Q", "star", "H"], "start_x": 3, "start_y": 4, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "square", "rotation": 180}, "BOTTOM": {"patternId": "H", "rotation": 270}, "FRONT": {"patternId": "E", "rotation": 0}, "BACK": {"patternId": "Q", "rotation": 270}, "LEFT": {"patternId": "star", "rotation": 180}, "RIGHT": {"patternId": "P", "rotation": 180}}, "bottom_faces": [{"patternId": "H", "rotation": 270, "x": 3, "y": 4}, {"patternId": "Q", "rotation": 90, "x": 3, "y": 3}, {"patternId": "P", "rotation": 0, "x": 4, "y": 3}, {"patternId": "square", "rotation": 90, "x": 4, "y": 2}, {"patternId": "Q", "rotation": 0, "x": 3, "y": 2}, {"patternId": "star", "rotation": 270, "x": 3, "y": 1}, {"patternId": "H", "rotation": 90, "x": 2, "y": 1}, {"patternId": "P", "rotation": 90, "x": 1, "y": 1}], "slot_sequence": ["BACK", "RIGHT", "TOP", "BACK", "LEFT", "BOTTOM", "RIGHT"], "required_slots": ["BACK", "RIGHT", "TOP", "LEFT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "square", "rotation": 180}, "BOTTOM": {"patternId": "H", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "Q", "rotation": 90}, "LEFT": {"patternId": "star", "rotation": 270}, "RIGHT": {"patternId": "P", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "square", "rotation": 180}, "BOTTOM": {"patternId": "H", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "Q", "rotation": 90}, "LEFT": {"patternId": "star", "rotation": 270}, "RIGHT": {"patternId": "P", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C233\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> N -> W -> N -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Q, rotation=90, flipVertical=true\n- step 2: patternId=P, rotation=0, flipVertical=true\n- step 3: patternId=square, rotation=90, flipVertical=true\n- step 4: patternId=Q, rotation=0, flipVertical=true\n- step 5: patternId=star, rotation=270, flipVertical=true\n- step 6: patternId=H, rotation=90, flipVertical=true\n- step 7: patternId=P, rotation=90, flipVertical=true\n- allowed patternId values for this task: Q, P, square, star, H, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C233"} +{"sample_id": "C234", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> S -> W -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "S", "W", "W", "S"], "observed_path_faces": [{"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C234_path_sequence.png"}, "metadata": {"level_id": 234, "name": "Reconstruct 234", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-234.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["O", "T", "1", "circle", "J", "V"], "start_x": 2, "start_y": 1, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "V", "rotation": 90}, "FRONT": {"patternId": "T", "rotation": 180}, "BACK": {"patternId": "circle", "rotation": 90}, "LEFT": {"patternId": "J", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 270}}, "bottom_faces": [{"patternId": "V", "rotation": 90, "x": 2, "y": 1}, {"patternId": "T", "rotation": 180, "x": 2, "y": 2}, {"patternId": "1", "rotation": 270, "x": 3, "y": 2}, {"patternId": "O", "rotation": 0, "x": 3, "y": 3}, {"patternId": "T", "rotation": 270, "x": 2, "y": 3}, {"patternId": "V", "rotation": 180, "x": 1, "y": 3}, {"patternId": "J", "rotation": 0, "x": 1, "y": 4}], "slot_sequence": ["FRONT", "RIGHT", "TOP", "FRONT", "BOTTOM", "LEFT"], "required_slots": ["FRONT", "RIGHT", "TOP", "BOTTOM", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "V", "rotation": 90}, "FRONT": {"patternId": "T", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "J", "rotation": 90}, "RIGHT": {"patternId": "1", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "V", "rotation": 90}, "FRONT": {"patternId": "T", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "J", "rotation": 90}, "RIGHT": {"patternId": "1", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C234\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> S -> W -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=T, rotation=180, flipVertical=true\n- step 2: patternId=1, rotation=270, flipVertical=true\n- step 3: patternId=O, rotation=0, flipVertical=true\n- step 4: patternId=T, rotation=270, flipVertical=true\n- step 5: patternId=V, rotation=180, flipVertical=true\n- step 6: patternId=J, rotation=0, flipVertical=true\n- allowed patternId values for this task: T, 1, O, V, J, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C234"} +{"sample_id": "C235", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> N -> N -> E -> W -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "N", "N", "E", "W", "E"], "observed_path_faces": [{"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C235_path_sequence.png"}, "metadata": {"level_id": 235, "name": "Reconstruct 235", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-235.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["G", "E", "square", "square", "K", "6"], "start_x": 1, "start_y": 2, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "G", "rotation": 270}, "BOTTOM": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "E", "rotation": 0}, "BACK": {"patternId": "square", "rotation": 0}, "LEFT": {"patternId": "K", "rotation": 180}, "RIGHT": {"patternId": "square", "rotation": 90}}, "bottom_faces": [{"patternId": "6", "rotation": 180, "x": 1, "y": 2}, {"patternId": "E", "rotation": 0, "x": 1, "y": 3}, {"patternId": "square", "rotation": 90, "x": 2, "y": 3}, {"patternId": "6", "rotation": 90, "x": 2, "y": 2}, {"patternId": "K", "rotation": 0, "x": 2, "y": 1}, {"patternId": "square", "rotation": 180, "x": 3, "y": 1}, {"patternId": "K", "rotation": 0, "x": 2, "y": 1}, {"patternId": "square", "rotation": 180, "x": 3, "y": 1}], "slot_sequence": ["FRONT", "RIGHT", "BOTTOM", "LEFT", "BACK", "LEFT", "BACK"], "required_slots": ["FRONT", "RIGHT", "BOTTOM", "LEFT", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "E", "rotation": 0}, "BACK": {"patternId": "square", "rotation": 180}, "LEFT": {"patternId": "K", "rotation": 270}, "RIGHT": {"patternId": "square", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "E", "rotation": 0}, "BACK": {"patternId": "square", "rotation": 180}, "LEFT": {"patternId": "K", "rotation": 270}, "RIGHT": {"patternId": "square", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C235\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> N -> N -> E -> W -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=E, rotation=0, flipVertical=true\n- step 2: patternId=square, rotation=90, flipVertical=true\n- step 3: patternId=6, rotation=90, flipVertical=true\n- step 4: patternId=K, rotation=0, flipVertical=true\n- step 5: patternId=square, rotation=180, flipVertical=true\n- step 6: patternId=K, rotation=0, flipVertical=true\n- step 7: patternId=square, rotation=180, flipVertical=true\n- allowed patternId values for this task: E, square, 6, K, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C235"} +{"sample_id": "C236", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> N -> E -> N -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "N", "E", "N", "S", "W"], "observed_path_faces": [{"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C236_path_sequence.png"}, "metadata": {"level_id": 236, "name": "Reconstruct 236", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-236.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["O", "5", "S", "J", "U", "1"], "start_x": 1, "start_y": 4, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "O", "rotation": 90}, "BOTTOM": {"patternId": "1", "rotation": 0}, "FRONT": {"patternId": "5", "rotation": 270}, "BACK": {"patternId": "J", "rotation": 180}, "LEFT": {"patternId": "U", "rotation": 180}, "RIGHT": {"patternId": "S", "rotation": 270}}, "bottom_faces": [{"patternId": "1", "rotation": 0, "x": 1, "y": 4}, {"patternId": "S", "rotation": 0, "x": 2, "y": 4}, {"patternId": "J", "rotation": 270, "x": 2, "y": 3}, {"patternId": "U", "rotation": 270, "x": 2, "y": 2}, {"patternId": "O", "rotation": 90, "x": 3, "y": 2}, {"patternId": "5", "rotation": 270, "x": 3, "y": 1}, {"patternId": "O", "rotation": 90, "x": 3, "y": 2}, {"patternId": "U", "rotation": 270, "x": 2, "y": 2}], "slot_sequence": ["RIGHT", "BACK", "LEFT", "TOP", "FRONT", "TOP", "LEFT"], "required_slots": ["RIGHT", "BACK", "LEFT", "TOP", "FRONT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "O", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "5", "rotation": 270}, "BACK": {"patternId": "J", "rotation": 0}, "LEFT": {"patternId": "U", "rotation": 270}, "RIGHT": {"patternId": "S", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "5", "rotation": 270}, "BACK": {"patternId": "J", "rotation": 0}, "LEFT": {"patternId": "U", "rotation": 270}, "RIGHT": {"patternId": "S", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C236\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> N -> E -> N -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=S, rotation=0, flipVertical=true\n- step 2: patternId=J, rotation=270, flipVertical=true\n- step 3: patternId=U, rotation=270, flipVertical=true\n- step 4: patternId=O, rotation=90, flipVertical=true\n- step 5: patternId=5, rotation=270, flipVertical=true\n- step 6: patternId=O, rotation=90, flipVertical=true\n- step 7: patternId=U, rotation=270, flipVertical=true\n- allowed patternId values for this task: S, J, U, O, 5, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C236"} +{"sample_id": "C237", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> S -> E -> N -> E -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "S", "E", "N", "E", "W"], "observed_path_faces": [{"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C237_path_sequence.png"}, "metadata": {"level_id": 237, "name": "Reconstruct 237", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-237.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["2", "2", "6", "N", "L", "W"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "2", "rotation": 270}, "BOTTOM": {"patternId": "W", "rotation": 90}, "FRONT": {"patternId": "2", "rotation": 0}, "BACK": {"patternId": "N", "rotation": 0}, "LEFT": {"patternId": "L", "rotation": 90}, "RIGHT": {"patternId": "6", "rotation": 180}}, "bottom_faces": [{"patternId": "W", "rotation": 90, "x": 1, "y": 1}, {"patternId": "2", "rotation": 0, "x": 1, "y": 2}, {"patternId": "2", "rotation": 270, "x": 1, "y": 3}, {"patternId": "N", "rotation": 180, "x": 1, "y": 4}, {"patternId": "6", "rotation": 0, "x": 2, "y": 4}, {"patternId": "2", "rotation": 180, "x": 2, "y": 3}, {"patternId": "2", "rotation": 270, "x": 3, "y": 3}, {"patternId": "2", "rotation": 180, "x": 2, "y": 3}], "slot_sequence": ["FRONT", "TOP", "BACK", "RIGHT", "TOP", "FRONT", "TOP"], "required_slots": ["FRONT", "TOP", "BACK", "RIGHT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "2", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 0}, "BACK": {"patternId": "N", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "2", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 0}, "BACK": {"patternId": "N", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C237\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> S -> E -> N -> E -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=2, rotation=0, flipVertical=true\n- step 2: patternId=2, rotation=270, flipVertical=true\n- step 3: patternId=N, rotation=180, flipVertical=true\n- step 4: patternId=6, rotation=0, flipVertical=true\n- step 5: patternId=2, rotation=180, flipVertical=true\n- step 6: patternId=2, rotation=270, flipVertical=true\n- step 7: patternId=2, rotation=180, flipVertical=true\n- allowed patternId values for this task: 2, N, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C237"} +{"sample_id": "C238", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> E -> E -> S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "E", "E", "S", "N"], "observed_path_faces": [{"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C238_path_sequence.png"}, "metadata": {"level_id": 238, "name": "Reconstruct 238", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-238.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["J", "N", "triangle", "V", "U", "M"], "start_x": 1, "start_y": 2, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "J", "rotation": 180}, "BOTTOM": {"patternId": "M", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 90}, "BACK": {"patternId": "V", "rotation": 0}, "LEFT": {"patternId": "U", "rotation": 90}, "RIGHT": {"patternId": "triangle", "rotation": 90}}, "bottom_faces": [{"patternId": "M", "rotation": 0, "x": 1, "y": 2}, {"patternId": "V", "rotation": 180, "x": 1, "y": 1}, {"patternId": "triangle", "rotation": 270, "x": 2, "y": 1}, {"patternId": "N", "rotation": 270, "x": 3, "y": 1}, {"patternId": "U", "rotation": 270, "x": 4, "y": 1}, {"patternId": "M", "rotation": 270, "x": 4, "y": 2}, {"patternId": "U", "rotation": 270, "x": 4, "y": 1}], "slot_sequence": ["BACK", "RIGHT", "FRONT", "LEFT", "BOTTOM", "LEFT"], "required_slots": ["BACK", "RIGHT", "FRONT", "LEFT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "M", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 90}, "BACK": {"patternId": "V", "rotation": 180}, "LEFT": {"patternId": "U", "rotation": 180}, "RIGHT": {"patternId": "triangle", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "M", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 90}, "BACK": {"patternId": "V", "rotation": 180}, "LEFT": {"patternId": "U", "rotation": 180}, "RIGHT": {"patternId": "triangle", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C238\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> E -> E -> S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=V, rotation=180, flipVertical=true\n- step 2: patternId=triangle, rotation=270, flipVertical=true\n- step 3: patternId=N, rotation=270, flipVertical=true\n- step 4: patternId=U, rotation=270, flipVertical=true\n- step 5: patternId=M, rotation=270, flipVertical=true\n- step 6: patternId=U, rotation=270, flipVertical=true\n- allowed patternId values for this task: V, triangle, N, U, M, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C238"} +{"sample_id": "C239", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> E -> N -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "E", "N", "W", "S"], "observed_path_faces": [{"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C239_path_sequence.png"}, "metadata": {"level_id": 239, "name": "Reconstruct 239", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-239.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["E", "B", "5", "C", "9", "Q"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "E", "rotation": 270}, "BOTTOM": {"patternId": "Q", "rotation": 90}, "FRONT": {"patternId": "B", "rotation": 180}, "BACK": {"patternId": "C", "rotation": 270}, "LEFT": {"patternId": "9", "rotation": 90}, "RIGHT": {"patternId": "5", "rotation": 0}}, "bottom_faces": [{"patternId": "Q", "rotation": 90, "x": 1, "y": 1}, {"patternId": "B", "rotation": 180, "x": 1, "y": 2}, {"patternId": "5", "rotation": 0, "x": 2, "y": 2}, {"patternId": "C", "rotation": 270, "x": 3, "y": 2}, {"patternId": "Q", "rotation": 270, "x": 3, "y": 1}, {"patternId": "5", "rotation": 270, "x": 2, "y": 1}, {"patternId": "C", "rotation": 180, "x": 2, "y": 2}], "slot_sequence": ["FRONT", "RIGHT", "BACK", "BOTTOM", "RIGHT", "BACK"], "required_slots": ["FRONT", "RIGHT", "BACK", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "Q", "rotation": 90}, "FRONT": {"patternId": "B", "rotation": 180}, "BACK": {"patternId": "C", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "5", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "Q", "rotation": 90}, "FRONT": {"patternId": "B", "rotation": 180}, "BACK": {"patternId": "C", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "5", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C239\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> E -> N -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=B, rotation=180, flipVertical=true\n- step 2: patternId=5, rotation=0, flipVertical=true\n- step 3: patternId=C, rotation=270, flipVertical=true\n- step 4: patternId=Q, rotation=270, flipVertical=true\n- step 5: patternId=5, rotation=270, flipVertical=true\n- step 6: patternId=C, rotation=180, flipVertical=true\n- allowed patternId values for this task: B, 5, C, Q, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C239"} +{"sample_id": "C240", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> S -> E -> E -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "S", "E", "E", "S", "W"], "observed_path_faces": [{"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C240_path_sequence.png"}, "metadata": {"level_id": 240, "name": "Reconstruct 240", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-240.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["H", "Y", "arrow_right", "arrow_left", "L", "P"], "start_x": 1, "start_y": 2, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "H", "rotation": 270}, "BOTTOM": {"patternId": "P", "rotation": 270}, "FRONT": {"patternId": "Y", "rotation": 270}, "BACK": {"patternId": "arrow_left", "rotation": 90}, "LEFT": {"patternId": "L", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}}, "bottom_faces": [{"patternId": "P", "rotation": 270, "x": 1, "y": 2}, {"patternId": "arrow_left", "rotation": 270, "x": 1, "y": 1}, {"patternId": "P", "rotation": 270, "x": 1, "y": 2}, {"patternId": "arrow_right", "rotation": 270, "x": 2, "y": 2}, {"patternId": "H", "rotation": 90, "x": 3, "y": 2}, {"patternId": "Y", "rotation": 90, "x": 3, "y": 3}, {"patternId": "arrow_right", "rotation": 0, "x": 2, "y": 3}], "slot_sequence": ["BACK", "BOTTOM", "RIGHT", "TOP", "FRONT", "RIGHT"], "required_slots": ["BACK", "BOTTOM", "RIGHT", "TOP", "FRONT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "H", "rotation": 270}, "BOTTOM": {"patternId": "P", "rotation": 270}, "FRONT": {"patternId": "Y", "rotation": 270}, "BACK": {"patternId": "arrow_left", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "H", "rotation": 270}, "BOTTOM": {"patternId": "P", "rotation": 270}, "FRONT": {"patternId": "Y", "rotation": 270}, "BACK": {"patternId": "arrow_left", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C240\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): N -> S -> E -> E -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_left, rotation=270, flipVertical=true\n- step 2: patternId=P, rotation=270, flipVertical=true\n- step 3: patternId=arrow_right, rotation=270, flipVertical=true\n- step 4: patternId=H, rotation=90, flipVertical=true\n- step 5: patternId=Y, rotation=90, flipVertical=true\n- step 6: patternId=arrow_right, rotation=0, flipVertical=true\n- allowed patternId values for this task: arrow_left, P, arrow_right, H, Y, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C240"} +{"sample_id": "C241", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> W -> N -> W -> S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "W", "N", "W", "S", "N"], "observed_path_faces": [{"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C241_path_sequence.png"}, "metadata": {"level_id": 241, "name": "Reconstruct 241", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-241.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["F", "G", "E", "J", "C", "3"], "start_x": 4, "start_y": 3, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "F", "rotation": 270}, "BOTTOM": {"patternId": "3", "rotation": 270}, "FRONT": {"patternId": "G", "rotation": 270}, "BACK": {"patternId": "J", "rotation": 0}, "LEFT": {"patternId": "C", "rotation": 270}, "RIGHT": {"patternId": "E", "rotation": 180}}, "bottom_faces": [{"patternId": "3", "rotation": 270, "x": 4, "y": 3}, {"patternId": "J", "rotation": 180, "x": 4, "y": 2}, {"patternId": "C", "rotation": 90, "x": 3, "y": 2}, {"patternId": "G", "rotation": 90, "x": 2, "y": 2}, {"patternId": "F", "rotation": 90, "x": 2, "y": 1}, {"patternId": "E", "rotation": 270, "x": 1, "y": 1}, {"patternId": "G", "rotation": 0, "x": 1, "y": 2}, {"patternId": "E", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["BACK", "LEFT", "FRONT", "TOP", "RIGHT", "FRONT", "RIGHT"], "required_slots": ["BACK", "LEFT", "FRONT", "TOP", "RIGHT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "F", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "G", "rotation": 270}, "BACK": {"patternId": "J", "rotation": 180}, "LEFT": {"patternId": "C", "rotation": 0}, "RIGHT": {"patternId": "E", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "F", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "G", "rotation": 270}, "BACK": {"patternId": "J", "rotation": 180}, "LEFT": {"patternId": "C", "rotation": 0}, "RIGHT": {"patternId": "E", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C241\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> W -> N -> W -> S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=J, rotation=180, flipVertical=true\n- step 2: patternId=C, rotation=90, flipVertical=true\n- step 3: patternId=G, rotation=90, flipVertical=true\n- step 4: patternId=F, rotation=90, flipVertical=true\n- step 5: patternId=E, rotation=270, flipVertical=true\n- step 6: patternId=G, rotation=0, flipVertical=true\n- step 7: patternId=E, rotation=270, flipVertical=true\n- allowed patternId values for this task: J, C, G, F, E, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C241"} +{"sample_id": "C242", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> E -> E -> N -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "E", "E", "N", "N", "N"], "observed_path_faces": [{"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C242_path_sequence.png"}, "metadata": {"level_id": 242, "name": "Reconstruct 242", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-242.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["star", "J", "E", "Z", "E", "2"], "start_x": 2, "start_y": 4, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "star", "rotation": 90}, "BOTTOM": {"patternId": "2", "rotation": 180}, "FRONT": {"patternId": "J", "rotation": 270}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "E", "rotation": 90}, "RIGHT": {"patternId": "E", "rotation": 180}}, "bottom_faces": [{"patternId": "2", "rotation": 180, "x": 2, "y": 4}, {"patternId": "E", "rotation": 0, "x": 1, "y": 4}, {"patternId": "2", "rotation": 180, "x": 2, "y": 4}, {"patternId": "E", "rotation": 270, "x": 3, "y": 4}, {"patternId": "Z", "rotation": 0, "x": 3, "y": 3}, {"patternId": "E", "rotation": 180, "x": 3, "y": 2}, {"patternId": "J", "rotation": 0, "x": 3, "y": 1}], "slot_sequence": ["LEFT", "BOTTOM", "RIGHT", "BACK", "LEFT", "FRONT"], "required_slots": ["LEFT", "BOTTOM", "RIGHT", "BACK", "FRONT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "2", "rotation": 180}, "FRONT": {"patternId": "J", "rotation": 270}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "E", "rotation": 180}, "RIGHT": {"patternId": "E", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "2", "rotation": 180}, "FRONT": {"patternId": "J", "rotation": 270}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "E", "rotation": 180}, "RIGHT": {"patternId": "E", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C242\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): W -> E -> E -> N -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=E, rotation=0, flipVertical=true\n- step 2: patternId=2, rotation=180, flipVertical=true\n- step 3: patternId=E, rotation=270, flipVertical=true\n- step 4: patternId=Z, rotation=0, flipVertical=true\n- step 5: patternId=E, rotation=180, flipVertical=true\n- step 6: patternId=J, rotation=0, flipVertical=true\n- allowed patternId values for this task: E, 2, Z, J, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C242"} +{"sample_id": "C243", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> S -> W -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "S", "W", "N", "W"], "observed_path_faces": [{"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C243_path_sequence.png"}, "metadata": {"level_id": 243, "name": "Reconstruct 243", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-243.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["B", "O", "5", "8", "arrow_down", "circle"], "start_x": 5, "start_y": 1, "grid_width": 7, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "B", "rotation": 270}, "BOTTOM": {"patternId": "circle", "rotation": 0}, "FRONT": {"patternId": "O", "rotation": 90}, "BACK": {"patternId": "8", "rotation": 270}, "LEFT": {"patternId": "arrow_down", "rotation": 180}, "RIGHT": {"patternId": "5", "rotation": 270}}, "bottom_faces": [{"patternId": "circle", "rotation": 0, "x": 5, "y": 1}, {"patternId": "arrow_down", "rotation": 90, "x": 4, "y": 1}, {"patternId": "B", "rotation": 90, "x": 3, "y": 1}, {"patternId": "O", "rotation": 270, "x": 3, "y": 2}, {"patternId": "5", "rotation": 90, "x": 2, "y": 2}, {"patternId": "B", "rotation": 180, "x": 2, "y": 1}, {"patternId": "8", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "TOP", "FRONT", "RIGHT", "TOP", "BACK"], "required_slots": ["LEFT", "TOP", "FRONT", "RIGHT", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "B", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "O", "rotation": 90}, "BACK": {"patternId": "8", "rotation": 90}, "LEFT": {"patternId": "arrow_down", "rotation": 270}, "RIGHT": {"patternId": "5", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "B", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "O", "rotation": 90}, "BACK": {"patternId": "8", "rotation": 90}, "LEFT": {"patternId": "arrow_down", "rotation": 270}, "RIGHT": {"patternId": "5", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C243\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> S -> W -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_down, rotation=90, flipVertical=true\n- step 2: patternId=B, rotation=90, flipVertical=true\n- step 3: patternId=O, rotation=270, flipVertical=true\n- step 4: patternId=5, rotation=90, flipVertical=true\n- step 5: patternId=B, rotation=180, flipVertical=true\n- step 6: patternId=8, rotation=0, flipVertical=true\n- allowed patternId values for this task: arrow_down, B, O, 5, 8, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C243"} +{"sample_id": "C244", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> W -> N -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "W", "N", "N", "E"], "observed_path_faces": [{"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C244_path_sequence.png"}, "metadata": {"level_id": 244, "name": "Reconstruct 244", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-244.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["L", "circle", "B", "X", "X", "square"], "start_x": 1, "start_y": 4, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "L", "rotation": 90}, "BOTTOM": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "circle", "rotation": 90}, "BACK": {"patternId": "X", "rotation": 180}, "LEFT": {"patternId": "X", "rotation": 270}, "RIGHT": {"patternId": "B", "rotation": 90}}, "bottom_faces": [{"patternId": "square", "rotation": 90, "x": 1, "y": 4}, {"patternId": "B", "rotation": 180, "x": 2, "y": 4}, {"patternId": "X", "rotation": 270, "x": 2, "y": 3}, {"patternId": "square", "rotation": 0, "x": 1, "y": 3}, {"patternId": "X", "rotation": 90, "x": 1, "y": 2}, {"patternId": "L", "rotation": 180, "x": 1, "y": 1}, {"patternId": "X", "rotation": 90, "x": 2, "y": 1}], "slot_sequence": ["RIGHT", "BACK", "BOTTOM", "LEFT", "TOP", "BACK"], "required_slots": ["RIGHT", "BACK", "BOTTOM", "LEFT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "L", "rotation": 90}, "BOTTOM": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "X", "rotation": 0}, "LEFT": {"patternId": "X", "rotation": 0}, "RIGHT": {"patternId": "B", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "L", "rotation": 90}, "BOTTOM": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "X", "rotation": 0}, "LEFT": {"patternId": "X", "rotation": 0}, "RIGHT": {"patternId": "B", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C244\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> W -> N -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=B, rotation=180, flipVertical=true\n- step 2: patternId=X, rotation=270, flipVertical=true\n- step 3: patternId=square, rotation=0, flipVertical=true\n- step 4: patternId=X, rotation=90, flipVertical=true\n- step 5: patternId=L, rotation=180, flipVertical=true\n- step 6: patternId=X, rotation=90, flipVertical=true\n- allowed patternId values for this task: B, X, square, L, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C244"} +{"sample_id": "C245", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> E -> N -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "E", "N", "N", "E"], "observed_path_faces": [{"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C245_path_sequence.png"}, "metadata": {"level_id": 245, "name": "Reconstruct 245", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-245.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["3", "I", "K", "D", "B", "plus"], "start_x": 1, "start_y": 2, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "3", "rotation": 270}, "BOTTOM": {"patternId": "plus", "rotation": 90}, "FRONT": {"patternId": "I", "rotation": 270}, "BACK": {"patternId": "D", "rotation": 180}, "LEFT": {"patternId": "B", "rotation": 270}, "RIGHT": {"patternId": "K", "rotation": 180}}, "bottom_faces": [{"patternId": "plus", "rotation": 90, "x": 1, "y": 2}, {"patternId": "K", "rotation": 270, "x": 2, "y": 2}, {"patternId": "I", "rotation": 0, "x": 2, "y": 3}, {"patternId": "3", "rotation": 0, "x": 3, "y": 3}, {"patternId": "K", "rotation": 180, "x": 3, "y": 2}, {"patternId": "plus", "rotation": 0, "x": 3, "y": 1}, {"patternId": "D", "rotation": 270, "x": 4, "y": 1}], "slot_sequence": ["RIGHT", "FRONT", "TOP", "RIGHT", "BOTTOM", "BACK"], "required_slots": ["RIGHT", "FRONT", "TOP", "BOTTOM", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "3", "rotation": 270}, "BOTTOM": {"patternId": "plus", "rotation": 90}, "FRONT": {"patternId": "I", "rotation": 270}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "K", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "3", "rotation": 270}, "BOTTOM": {"patternId": "plus", "rotation": 90}, "FRONT": {"patternId": "I", "rotation": 270}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "K", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C245\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> E -> N -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=K, rotation=270, flipVertical=true\n- step 2: patternId=I, rotation=0, flipVertical=true\n- step 3: patternId=3, rotation=0, flipVertical=true\n- step 4: patternId=K, rotation=180, flipVertical=true\n- step 5: patternId=plus, rotation=0, flipVertical=true\n- step 6: patternId=D, rotation=270, flipVertical=true\n- allowed patternId values for this task: K, I, 3, plus, D, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C245"} +{"sample_id": "C246", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> W -> W -> E -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "W", "W", "E", "N", "N"], "observed_path_faces": [{"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C246_path_sequence.png"}, "metadata": {"level_id": 246, "name": "Reconstruct 246", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-246.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["M", "heart", "M", "4", "4", "diamond"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "M", "rotation": 0}, "BOTTOM": {"patternId": "diamond", "rotation": 90}, "FRONT": {"patternId": "heart", "rotation": 0}, "BACK": {"patternId": "4", "rotation": 270}, "LEFT": {"patternId": "4", "rotation": 180}, "RIGHT": {"patternId": "M", "rotation": 90}}, "bottom_faces": [{"patternId": "diamond", "rotation": 90, "x": 3, "y": 1}, {"patternId": "heart", "rotation": 0, "x": 3, "y": 2}, {"patternId": "M", "rotation": 0, "x": 3, "y": 3}, {"patternId": "4", "rotation": 270, "x": 2, "y": 3}, {"patternId": "diamond", "rotation": 270, "x": 1, "y": 3}, {"patternId": "4", "rotation": 270, "x": 2, "y": 3}, {"patternId": "heart", "rotation": 90, "x": 2, "y": 2}, {"patternId": "M", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["FRONT", "TOP", "LEFT", "BOTTOM", "LEFT", "FRONT", "RIGHT"], "required_slots": ["FRONT", "TOP", "LEFT", "BOTTOM", "RIGHT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "M", "rotation": 0}, "BOTTOM": {"patternId": "diamond", "rotation": 90}, "FRONT": {"patternId": "heart", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "4", "rotation": 270}, "RIGHT": {"patternId": "M", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 0}, "BOTTOM": {"patternId": "diamond", "rotation": 90}, "FRONT": {"patternId": "heart", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "4", "rotation": 270}, "RIGHT": {"patternId": "M", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C246\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> W -> W -> E -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=heart, rotation=0, flipVertical=true\n- step 2: patternId=M, rotation=0, flipVertical=true\n- step 3: patternId=4, rotation=270, flipVertical=true\n- step 4: patternId=diamond, rotation=270, flipVertical=true\n- step 5: patternId=4, rotation=270, flipVertical=true\n- step 6: patternId=heart, rotation=90, flipVertical=true\n- step 7: patternId=M, rotation=180, flipVertical=true\n- allowed patternId values for this task: heart, M, 4, diamond, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C246"} +{"sample_id": "C247", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> S -> E -> N -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "S", "E", "N", "W", "S"], "observed_path_faces": [{"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C247_path_sequence.png"}, "metadata": {"level_id": 247, "name": "Reconstruct 247", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-247.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["4", "5", "F", "star", "N", "5"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "4", "rotation": 90}, "BOTTOM": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "5", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 90}, "LEFT": {"patternId": "N", "rotation": 0}, "RIGHT": {"patternId": "F", "rotation": 90}}, "bottom_faces": [{"patternId": "5", "rotation": 90, "x": 1, "y": 1}, {"patternId": "F", "rotation": 180, "x": 2, "y": 1}, {"patternId": "5", "rotation": 90, "x": 2, "y": 2}, {"patternId": "N", "rotation": 90, "x": 2, "y": 3}, {"patternId": "4", "rotation": 90, "x": 3, "y": 3}, {"patternId": "5", "rotation": 0, "x": 3, "y": 2}, {"patternId": "N", "rotation": 0, "x": 2, "y": 2}, {"patternId": "4", "rotation": 0, "x": 2, "y": 3}], "slot_sequence": ["RIGHT", "FRONT", "LEFT", "TOP", "FRONT", "LEFT", "TOP"], "required_slots": ["RIGHT", "FRONT", "LEFT", "TOP"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "4", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "5", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "N", "rotation": 90}, "RIGHT": {"patternId": "F", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "4", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "5", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "N", "rotation": 90}, "RIGHT": {"patternId": "F", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C247\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> S -> E -> N -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=F, rotation=180, flipVertical=true\n- step 2: patternId=5, rotation=90, flipVertical=true\n- step 3: patternId=N, rotation=90, flipVertical=true\n- step 4: patternId=4, rotation=90, flipVertical=true\n- step 5: patternId=5, rotation=0, flipVertical=true\n- step 6: patternId=N, rotation=0, flipVertical=true\n- step 7: patternId=4, rotation=0, flipVertical=true\n- allowed patternId values for this task: F, 5, N, 4, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C247"} +{"sample_id": "C248", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> E -> N -> N -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "E", "N", "N", "N", "E"], "observed_path_faces": [{"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C248_path_sequence.png"}, "metadata": {"level_id": 248, "name": "Reconstruct 248", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-248.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["F", "square", "arrow_up", "star", "P", "W"], "start_x": 1, "start_y": 5, "grid_width": 6, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "F", "rotation": 180}, "BOTTOM": {"patternId": "W", "rotation": 180}, "FRONT": {"patternId": "square", "rotation": 270}, "BACK": {"patternId": "star", "rotation": 180}, "LEFT": {"patternId": "P", "rotation": 90}, "RIGHT": {"patternId": "arrow_up", "rotation": 270}}, "bottom_faces": [{"patternId": "W", "rotation": 180, "x": 1, "y": 5}, {"patternId": "star", "rotation": 0, "x": 1, "y": 4}, {"patternId": "arrow_up", "rotation": 90, "x": 2, "y": 4}, {"patternId": "square", "rotation": 90, "x": 3, "y": 4}, {"patternId": "F", "rotation": 0, "x": 3, "y": 3}, {"patternId": "star", "rotation": 180, "x": 3, "y": 2}, {"patternId": "W", "rotation": 0, "x": 3, "y": 1}, {"patternId": "P", "rotation": 180, "x": 4, "y": 1}], "slot_sequence": ["BACK", "RIGHT", "FRONT", "TOP", "BACK", "BOTTOM", "LEFT"], "required_slots": ["BACK", "RIGHT", "FRONT", "TOP", "BOTTOM", "LEFT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "F", "rotation": 180}, "BOTTOM": {"patternId": "W", "rotation": 180}, "FRONT": {"patternId": "square", "rotation": 270}, "BACK": {"patternId": "star", "rotation": 0}, "LEFT": {"patternId": "P", "rotation": 180}, "RIGHT": {"patternId": "arrow_up", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "F", "rotation": 180}, "BOTTOM": {"patternId": "W", "rotation": 180}, "FRONT": {"patternId": "square", "rotation": 270}, "BACK": {"patternId": "star", "rotation": 0}, "LEFT": {"patternId": "P", "rotation": 180}, "RIGHT": {"patternId": "arrow_up", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C248\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> E -> N -> N -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=star, rotation=0, flipVertical=true\n- step 2: patternId=arrow_up, rotation=90, flipVertical=true\n- step 3: patternId=square, rotation=90, flipVertical=true\n- step 4: patternId=F, rotation=0, flipVertical=true\n- step 5: patternId=star, rotation=180, flipVertical=true\n- step 6: patternId=W, rotation=0, flipVertical=true\n- step 7: patternId=P, rotation=180, flipVertical=true\n- allowed patternId values for this task: star, arrow_up, square, F, W, P, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C248"} +{"sample_id": "C249", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> W -> S -> W -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "W", "S", "W", "E", "E"], "observed_path_faces": [{"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C249_path_sequence.png"}, "metadata": {"level_id": 249, "name": "Reconstruct 249", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-249.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["2", "X", "O", "O", "heart", "arrow_right"], "start_x": 5, "start_y": 1, "grid_width": 7, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "2", "rotation": 90}, "BOTTOM": {"patternId": "arrow_right", "rotation": 90}, "FRONT": {"patternId": "X", "rotation": 90}, "BACK": {"patternId": "O", "rotation": 180}, "LEFT": {"patternId": "heart", "rotation": 180}, "RIGHT": {"patternId": "O", "rotation": 180}}, "bottom_faces": [{"patternId": "arrow_right", "rotation": 90, "x": 5, "y": 1}, {"patternId": "heart", "rotation": 90, "x": 4, "y": 1}, {"patternId": "2", "rotation": 270, "x": 3, "y": 1}, {"patternId": "O", "rotation": 270, "x": 2, "y": 1}, {"patternId": "X", "rotation": 180, "x": 2, "y": 2}, {"patternId": "arrow_right", "rotation": 180, "x": 1, "y": 2}, {"patternId": "X", "rotation": 180, "x": 2, "y": 2}, {"patternId": "2", "rotation": 180, "x": 3, "y": 2}], "slot_sequence": ["LEFT", "TOP", "RIGHT", "FRONT", "BOTTOM", "FRONT", "TOP"], "required_slots": ["LEFT", "TOP", "RIGHT", "FRONT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "2", "rotation": 90}, "BOTTOM": {"patternId": "arrow_right", "rotation": 90}, "FRONT": {"patternId": "X", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 270}, "RIGHT": {"patternId": "O", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "2", "rotation": 90}, "BOTTOM": {"patternId": "arrow_right", "rotation": 90}, "FRONT": {"patternId": "X", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 270}, "RIGHT": {"patternId": "O", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C249\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> W -> S -> W -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=heart, rotation=90, flipVertical=true\n- step 2: patternId=2, rotation=270, flipVertical=true\n- step 3: patternId=O, rotation=270, flipVertical=true\n- step 4: patternId=X, rotation=180, flipVertical=true\n- step 5: patternId=arrow_right, rotation=180, flipVertical=true\n- step 6: patternId=X, rotation=180, flipVertical=true\n- step 7: patternId=2, rotation=180, flipVertical=true\n- allowed patternId values for this task: heart, 2, O, X, arrow_right, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C249"} +{"sample_id": "C250", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> N -> W -> N -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "N", "W", "N", "W", "N"], "observed_path_faces": [{"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C250_path_sequence.png"}, "metadata": {"level_id": 250, "name": "Reconstruct 250", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-250.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["B", "1", "O", "smile", "M", "2"], "start_x": 2, "start_y": 5, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "B", "rotation": 0}, "BOTTOM": {"patternId": "2", "rotation": 0}, "FRONT": {"patternId": "1", "rotation": 0}, "BACK": {"patternId": "smile", "rotation": 270}, "LEFT": {"patternId": "M", "rotation": 180}, "RIGHT": {"patternId": "O", "rotation": 180}}, "bottom_faces": [{"patternId": "2", "rotation": 0, "x": 2, "y": 5}, {"patternId": "O", "rotation": 270, "x": 3, "y": 5}, {"patternId": "smile", "rotation": 0, "x": 3, "y": 4}, {"patternId": "M", "rotation": 270, "x": 3, "y": 3}, {"patternId": "2", "rotation": 180, "x": 2, "y": 3}, {"patternId": "1", "rotation": 180, "x": 2, "y": 2}, {"patternId": "O", "rotation": 0, "x": 1, "y": 2}, {"patternId": "B", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["RIGHT", "BACK", "LEFT", "BOTTOM", "FRONT", "RIGHT", "TOP"], "required_slots": ["RIGHT", "BACK", "LEFT", "BOTTOM", "FRONT", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "B", "rotation": 0}, "BOTTOM": {"patternId": "2", "rotation": 0}, "FRONT": {"patternId": "1", "rotation": 0}, "BACK": {"patternId": "smile", "rotation": 90}, "LEFT": {"patternId": "M", "rotation": 270}, "RIGHT": {"patternId": "O", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "B", "rotation": 0}, "BOTTOM": {"patternId": "2", "rotation": 0}, "FRONT": {"patternId": "1", "rotation": 0}, "BACK": {"patternId": "smile", "rotation": 90}, "LEFT": {"patternId": "M", "rotation": 270}, "RIGHT": {"patternId": "O", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C250\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> N -> W -> N -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=O, rotation=270, flipVertical=true\n- step 2: patternId=smile, rotation=0, flipVertical=true\n- step 3: patternId=M, rotation=270, flipVertical=true\n- step 4: patternId=2, rotation=180, flipVertical=true\n- step 5: patternId=1, rotation=180, flipVertical=true\n- step 6: patternId=O, rotation=0, flipVertical=true\n- step 7: patternId=B, rotation=270, flipVertical=true\n- allowed patternId values for this task: O, smile, M, 2, 1, B, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C250"} +{"sample_id": "C251", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> W -> W -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "W", "W", "S", "S"], "observed_path_faces": [{"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C251_path_sequence.png"}, "metadata": {"level_id": 251, "name": "Reconstruct 251", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-251.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["A", "A", "D", "9", "V", "H"], "start_x": 2, "start_y": 2, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "A", "rotation": 270}, "BOTTOM": {"patternId": "H", "rotation": 270}, "FRONT": {"patternId": "A", "rotation": 270}, "BACK": {"patternId": "9", "rotation": 0}, "LEFT": {"patternId": "V", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 270}}, "bottom_faces": [{"patternId": "H", "rotation": 270, "x": 2, "y": 2}, {"patternId": "9", "rotation": 180, "x": 2, "y": 1}, {"patternId": "D", "rotation": 90, "x": 3, "y": 1}, {"patternId": "9", "rotation": 180, "x": 2, "y": 1}, {"patternId": "V", "rotation": 180, "x": 1, "y": 1}, {"patternId": "H", "rotation": 180, "x": 1, "y": 2}, {"patternId": "D", "rotation": 270, "x": 1, "y": 3}], "slot_sequence": ["BACK", "RIGHT", "BACK", "LEFT", "BOTTOM", "RIGHT"], "required_slots": ["BACK", "RIGHT", "LEFT", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "H", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "9", "rotation": 180}, "LEFT": {"patternId": "V", "rotation": 90}, "RIGHT": {"patternId": "D", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "H", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "9", "rotation": 180}, "LEFT": {"patternId": "V", "rotation": 90}, "RIGHT": {"patternId": "D", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C251\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> W -> W -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=9, rotation=180, flipVertical=true\n- step 2: patternId=D, rotation=90, flipVertical=true\n- step 3: patternId=9, rotation=180, flipVertical=true\n- step 4: patternId=V, rotation=180, flipVertical=true\n- step 5: patternId=H, rotation=180, flipVertical=true\n- step 6: patternId=D, rotation=270, flipVertical=true\n- allowed patternId values for this task: 9, D, V, H, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C251"} +{"sample_id": "C252", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> S -> S -> S -> E -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "S", "S", "S", "E", "W"], "observed_path_faces": [{"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C252_path_sequence.png"}, "metadata": {"level_id": 252, "name": "Reconstruct 252", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-252.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["O", "C", "I", "smile", "S", "A"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "O", "rotation": 0}, "BOTTOM": {"patternId": "A", "rotation": 270}, "FRONT": {"patternId": "C", "rotation": 90}, "BACK": {"patternId": "smile", "rotation": 180}, "LEFT": {"patternId": "S", "rotation": 180}, "RIGHT": {"patternId": "I", "rotation": 0}}, "bottom_faces": [{"patternId": "A", "rotation": 270, "x": 1, "y": 2}, {"patternId": "smile", "rotation": 0, "x": 1, "y": 1}, {"patternId": "A", "rotation": 270, "x": 1, "y": 2}, {"patternId": "C", "rotation": 90, "x": 1, "y": 3}, {"patternId": "O", "rotation": 0, "x": 1, "y": 4}, {"patternId": "I", "rotation": 270, "x": 2, "y": 4}, {"patternId": "O", "rotation": 0, "x": 1, "y": 4}], "slot_sequence": ["BACK", "BOTTOM", "FRONT", "TOP", "RIGHT", "TOP"], "required_slots": ["BACK", "BOTTOM", "FRONT", "TOP", "RIGHT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "O", "rotation": 0}, "BOTTOM": {"patternId": "A", "rotation": 270}, "FRONT": {"patternId": "C", "rotation": 90}, "BACK": {"patternId": "smile", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 0}, "BOTTOM": {"patternId": "A", "rotation": 270}, "FRONT": {"patternId": "C", "rotation": 90}, "BACK": {"patternId": "smile", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C252\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): N -> S -> S -> S -> E -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=smile, rotation=0, flipVertical=true\n- step 2: patternId=A, rotation=270, flipVertical=true\n- step 3: patternId=C, rotation=90, flipVertical=true\n- step 4: patternId=O, rotation=0, flipVertical=true\n- step 5: patternId=I, rotation=270, flipVertical=true\n- step 6: patternId=O, rotation=0, flipVertical=true\n- allowed patternId values for this task: smile, A, C, O, I, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C252"} +{"sample_id": "C253", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> E -> E -> N -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "E", "E", "N", "N", "W"], "observed_path_faces": [{"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C253_path_sequence.png"}, "metadata": {"level_id": 253, "name": "Reconstruct 253", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-253.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["4", "plus", "B", "6", "E", "H"], "start_x": 1, "start_y": 5, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "4", "rotation": 270}, "BOTTOM": {"patternId": "H", "rotation": 0}, "FRONT": {"patternId": "plus", "rotation": 90}, "BACK": {"patternId": "6", "rotation": 180}, "LEFT": {"patternId": "E", "rotation": 180}, "RIGHT": {"patternId": "B", "rotation": 180}}, "bottom_faces": [{"patternId": "H", "rotation": 0, "x": 1, "y": 5}, {"patternId": "6", "rotation": 0, "x": 1, "y": 4}, {"patternId": "4", "rotation": 270, "x": 1, "y": 3}, {"patternId": "B", "rotation": 90, "x": 2, "y": 3}, {"patternId": "H", "rotation": 180, "x": 3, "y": 3}, {"patternId": "plus", "rotation": 270, "x": 3, "y": 2}, {"patternId": "4", "rotation": 90, "x": 3, "y": 1}, {"patternId": "B", "rotation": 270, "x": 2, "y": 1}], "slot_sequence": ["BACK", "TOP", "RIGHT", "BOTTOM", "FRONT", "TOP", "RIGHT"], "required_slots": ["BACK", "TOP", "RIGHT", "BOTTOM", "FRONT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "4", "rotation": 270}, "BOTTOM": {"patternId": "H", "rotation": 0}, "FRONT": {"patternId": "plus", "rotation": 90}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "B", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "4", "rotation": 270}, "BOTTOM": {"patternId": "H", "rotation": 0}, "FRONT": {"patternId": "plus", "rotation": 90}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "B", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C253\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> E -> E -> N -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=6, rotation=0, flipVertical=true\n- step 2: patternId=4, rotation=270, flipVertical=true\n- step 3: patternId=B, rotation=90, flipVertical=true\n- step 4: patternId=H, rotation=180, flipVertical=true\n- step 5: patternId=plus, rotation=270, flipVertical=true\n- step 6: patternId=4, rotation=90, flipVertical=true\n- step 7: patternId=B, rotation=270, flipVertical=true\n- allowed patternId values for this task: 6, 4, B, H, plus, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C253"} +{"sample_id": "C254", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> W -> S -> E -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "W", "S", "E", "S", "S"], "observed_path_faces": [{"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C254_path_sequence.png"}, "metadata": {"level_id": 254, "name": "Reconstruct 254", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-254.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["star", "4", "circle", "M", "heart", "star"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "star", "rotation": 270}, "BOTTOM": {"patternId": "star", "rotation": 180}, "FRONT": {"patternId": "4", "rotation": 180}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 0}, "RIGHT": {"patternId": "circle", "rotation": 180}}, "bottom_faces": [{"patternId": "star", "rotation": 180, "x": 1, "y": 1}, {"patternId": "circle", "rotation": 270, "x": 2, "y": 1}, {"patternId": "star", "rotation": 180, "x": 1, "y": 1}, {"patternId": "4", "rotation": 180, "x": 1, "y": 2}, {"patternId": "circle", "rotation": 180, "x": 2, "y": 2}, {"patternId": "star", "rotation": 0, "x": 2, "y": 3}, {"patternId": "heart", "rotation": 180, "x": 2, "y": 4}], "slot_sequence": ["RIGHT", "BOTTOM", "FRONT", "RIGHT", "TOP", "LEFT"], "required_slots": ["RIGHT", "BOTTOM", "FRONT", "TOP", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "star", "rotation": 270}, "BOTTOM": {"patternId": "star", "rotation": 180}, "FRONT": {"patternId": "4", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 90}, "RIGHT": {"patternId": "circle", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 270}, "BOTTOM": {"patternId": "star", "rotation": 180}, "FRONT": {"patternId": "4", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 90}, "RIGHT": {"patternId": "circle", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C254\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): E -> W -> S -> E -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=circle, rotation=270, flipVertical=true\n- step 2: patternId=star, rotation=180, flipVertical=true\n- step 3: patternId=4, rotation=180, flipVertical=true\n- step 4: patternId=circle, rotation=180, flipVertical=true\n- step 5: patternId=star, rotation=0, flipVertical=true\n- step 6: patternId=heart, rotation=180, flipVertical=true\n- allowed patternId values for this task: circle, star, 4, heart, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C254"} +{"sample_id": "C255", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> W -> E -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "W", "E", "E", "E"], "observed_path_faces": [{"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C255_path_sequence.png"}, "metadata": {"level_id": 255, "name": "Reconstruct 255", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-255.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["3", "9", "arrow_down", "B", "I", "4"], "start_x": 2, "start_y": 1, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "3", "rotation": 270}, "BOTTOM": {"patternId": "4", "rotation": 90}, "FRONT": {"patternId": "9", "rotation": 270}, "BACK": {"patternId": "B", "rotation": 270}, "LEFT": {"patternId": "I", "rotation": 0}, "RIGHT": {"patternId": "arrow_down", "rotation": 90}}, "bottom_faces": [{"patternId": "4", "rotation": 90, "x": 2, "y": 1}, {"patternId": "9", "rotation": 270, "x": 2, "y": 2}, {"patternId": "3", "rotation": 270, "x": 2, "y": 3}, {"patternId": "I", "rotation": 90, "x": 1, "y": 3}, {"patternId": "3", "rotation": 270, "x": 2, "y": 3}, {"patternId": "arrow_down", "rotation": 0, "x": 3, "y": 3}, {"patternId": "4", "rotation": 270, "x": 4, "y": 3}], "slot_sequence": ["FRONT", "TOP", "LEFT", "TOP", "RIGHT", "BOTTOM"], "required_slots": ["FRONT", "TOP", "LEFT", "RIGHT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "3", "rotation": 270}, "BOTTOM": {"patternId": "4", "rotation": 90}, "FRONT": {"patternId": "9", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "I", "rotation": 90}, "RIGHT": {"patternId": "arrow_down", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "3", "rotation": 270}, "BOTTOM": {"patternId": "4", "rotation": 90}, "FRONT": {"patternId": "9", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "I", "rotation": 90}, "RIGHT": {"patternId": "arrow_down", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C255\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> W -> E -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=9, rotation=270, flipVertical=true\n- step 2: patternId=3, rotation=270, flipVertical=true\n- step 3: patternId=I, rotation=90, flipVertical=true\n- step 4: patternId=3, rotation=270, flipVertical=true\n- step 5: patternId=arrow_down, rotation=0, flipVertical=true\n- step 6: patternId=4, rotation=270, flipVertical=true\n- allowed patternId values for this task: 9, 3, I, arrow_down, 4, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C255"} +{"sample_id": "C256", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> N -> E -> S -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "N", "E", "S", "W", "W"], "observed_path_faces": [{"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C256_path_sequence.png"}, "metadata": {"level_id": 256, "name": "Reconstruct 256", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-256.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["A", "R", "R", "X", "E", "Z"], "start_x": 2, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "A", "rotation": 90}, "BOTTOM": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "R", "rotation": 0}, "BACK": {"patternId": "X", "rotation": 90}, "LEFT": {"patternId": "E", "rotation": 90}, "RIGHT": {"patternId": "R", "rotation": 0}}, "bottom_faces": [{"patternId": "Z", "rotation": 270, "x": 2, "y": 1}, {"patternId": "R", "rotation": 0, "x": 2, "y": 2}, {"patternId": "Z", "rotation": 270, "x": 2, "y": 1}, {"patternId": "R", "rotation": 90, "x": 3, "y": 1}, {"patternId": "R", "rotation": 90, "x": 3, "y": 2}, {"patternId": "Z", "rotation": 0, "x": 2, "y": 2}, {"patternId": "X", "rotation": 0, "x": 1, "y": 2}], "slot_sequence": ["FRONT", "BOTTOM", "RIGHT", "FRONT", "BOTTOM", "BACK"], "required_slots": ["FRONT", "BOTTOM", "RIGHT", "BACK"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "R", "rotation": 0}, "BACK": {"patternId": "X", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "R", "rotation": 0}, "BACK": {"patternId": "X", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C256\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): S -> N -> E -> S -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=R, rotation=0, flipVertical=true\n- step 2: patternId=Z, rotation=270, flipVertical=true\n- step 3: patternId=R, rotation=90, flipVertical=true\n- step 4: patternId=R, rotation=90, flipVertical=true\n- step 5: patternId=Z, rotation=0, flipVertical=true\n- step 6: patternId=X, rotation=0, flipVertical=true\n- allowed patternId values for this task: R, Z, X, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C256"} +{"sample_id": "C257", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> S -> S -> E -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "S", "S", "E", "N", "E"], "observed_path_faces": [{"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C257_path_sequence.png"}, "metadata": {"level_id": 257, "name": "Reconstruct 257", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-257.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["4", "heart", "M", "arrow_left", "6", "S"], "start_x": 2, "start_y": 1, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "4", "rotation": 90}, "BOTTOM": {"patternId": "S", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 180}, "BACK": {"patternId": "arrow_left", "rotation": 270}, "LEFT": {"patternId": "6", "rotation": 90}, "RIGHT": {"patternId": "M", "rotation": 180}}, "bottom_faces": [{"patternId": "S", "rotation": 0, "x": 2, "y": 1}, {"patternId": "6", "rotation": 0, "x": 1, "y": 1}, {"patternId": "heart", "rotation": 90, "x": 1, "y": 2}, {"patternId": "M", "rotation": 90, "x": 1, "y": 3}, {"patternId": "arrow_left", "rotation": 180, "x": 1, "y": 4}, {"patternId": "S", "rotation": 90, "x": 2, "y": 4}, {"patternId": "M", "rotation": 0, "x": 2, "y": 3}, {"patternId": "heart", "rotation": 0, "x": 3, "y": 3}], "slot_sequence": ["LEFT", "FRONT", "RIGHT", "BACK", "BOTTOM", "RIGHT", "FRONT"], "required_slots": ["LEFT", "FRONT", "RIGHT", "BACK", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "S", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 180}, "BACK": {"patternId": "arrow_left", "rotation": 90}, "LEFT": {"patternId": "6", "rotation": 180}, "RIGHT": {"patternId": "M", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "S", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 180}, "BACK": {"patternId": "arrow_left", "rotation": 90}, "LEFT": {"patternId": "6", "rotation": 180}, "RIGHT": {"patternId": "M", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C257\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> S -> S -> E -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=6, rotation=0, flipVertical=true\n- step 2: patternId=heart, rotation=90, flipVertical=true\n- step 3: patternId=M, rotation=90, flipVertical=true\n- step 4: patternId=arrow_left, rotation=180, flipVertical=true\n- step 5: patternId=S, rotation=90, flipVertical=true\n- step 6: patternId=M, rotation=0, flipVertical=true\n- step 7: patternId=heart, rotation=0, flipVertical=true\n- allowed patternId values for this task: 6, heart, M, arrow_left, S, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C257"} +{"sample_id": "C258", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> S -> N -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "S", "N", "N", "E"], "observed_path_faces": [{"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C258_path_sequence.png"}, "metadata": {"level_id": 258, "name": "Reconstruct 258", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-258.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["E", "W", "1", "U", "Z", "H"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "E", "rotation": 90}, "BOTTOM": {"patternId": "H", "rotation": 270}, "FRONT": {"patternId": "W", "rotation": 0}, "BACK": {"patternId": "U", "rotation": 270}, "LEFT": {"patternId": "Z", "rotation": 180}, "RIGHT": {"patternId": "1", "rotation": 0}}, "bottom_faces": [{"patternId": "H", "rotation": 270, "x": 1, "y": 1}, {"patternId": "W", "rotation": 0, "x": 1, "y": 2}, {"patternId": "1", "rotation": 0, "x": 2, "y": 2}, {"patternId": "E", "rotation": 180, "x": 2, "y": 3}, {"patternId": "1", "rotation": 0, "x": 2, "y": 2}, {"patternId": "H", "rotation": 180, "x": 2, "y": 1}, {"patternId": "U", "rotation": 0, "x": 3, "y": 1}], "slot_sequence": ["FRONT", "RIGHT", "TOP", "RIGHT", "BOTTOM", "BACK"], "required_slots": ["FRONT", "RIGHT", "TOP", "BOTTOM", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "E", "rotation": 90}, "BOTTOM": {"patternId": "H", "rotation": 270}, "FRONT": {"patternId": "W", "rotation": 0}, "BACK": {"patternId": "U", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "E", "rotation": 90}, "BOTTOM": {"patternId": "H", "rotation": 270}, "FRONT": {"patternId": "W", "rotation": 0}, "BACK": {"patternId": "U", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C258\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> S -> N -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=W, rotation=0, flipVertical=true\n- step 2: patternId=1, rotation=0, flipVertical=true\n- step 3: patternId=E, rotation=180, flipVertical=true\n- step 4: patternId=1, rotation=0, flipVertical=true\n- step 5: patternId=H, rotation=180, flipVertical=true\n- step 6: patternId=U, rotation=0, flipVertical=true\n- allowed patternId values for this task: W, 1, E, H, U, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C258"} +{"sample_id": "C259", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> E -> S -> W -> E -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "E", "S", "W", "E", "E", "E"], "observed_path_faces": [{"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C259_path_sequence.png"}, "metadata": {"level_id": 259, "name": "Reconstruct 259", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-259.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["E", "L", "E", "M", "8", "arrow_down"], "start_x": 2, "start_y": 1, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "E", "rotation": 90}, "BOTTOM": {"patternId": "arrow_down", "rotation": 270}, "FRONT": {"patternId": "L", "rotation": 180}, "BACK": {"patternId": "M", "rotation": 180}, "LEFT": {"patternId": "8", "rotation": 180}, "RIGHT": {"patternId": "E", "rotation": 180}}, "bottom_faces": [{"patternId": "arrow_down", "rotation": 270, "x": 2, "y": 1}, {"patternId": "8", "rotation": 90, "x": 1, "y": 1}, {"patternId": "arrow_down", "rotation": 270, "x": 2, "y": 1}, {"patternId": "L", "rotation": 180, "x": 2, "y": 2}, {"patternId": "8", "rotation": 180, "x": 1, "y": 2}, {"patternId": "L", "rotation": 180, "x": 2, "y": 2}, {"patternId": "E", "rotation": 180, "x": 3, "y": 2}, {"patternId": "M", "rotation": 180, "x": 4, "y": 2}], "slot_sequence": ["LEFT", "BOTTOM", "FRONT", "LEFT", "FRONT", "RIGHT", "BACK"], "required_slots": ["LEFT", "BOTTOM", "FRONT", "RIGHT", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_down", "rotation": 270}, "FRONT": {"patternId": "L", "rotation": 180}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 270}, "RIGHT": {"patternId": "E", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_down", "rotation": 270}, "FRONT": {"patternId": "L", "rotation": 180}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 270}, "RIGHT": {"patternId": "E", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C259\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): W -> E -> S -> W -> E -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=8, rotation=90, flipVertical=true\n- step 2: patternId=arrow_down, rotation=270, flipVertical=true\n- step 3: patternId=L, rotation=180, flipVertical=true\n- step 4: patternId=8, rotation=180, flipVertical=true\n- step 5: patternId=L, rotation=180, flipVertical=true\n- step 6: patternId=E, rotation=180, flipVertical=true\n- step 7: patternId=M, rotation=180, flipVertical=true\n- allowed patternId values for this task: 8, arrow_down, L, E, M, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C259"} +{"sample_id": "C260", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> S -> W -> S -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "S", "W", "S", "S", "W"], "observed_path_faces": [{"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C260_path_sequence.png"}, "metadata": {"level_id": 260, "name": "Reconstruct 260", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-260.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["9", "C", "circle", "triangle", "U", "A"], "start_x": 4, "start_y": 2, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "9", "rotation": 90}, "BOTTOM": {"patternId": "A", "rotation": 180}, "FRONT": {"patternId": "C", "rotation": 180}, "BACK": {"patternId": "triangle", "rotation": 270}, "LEFT": {"patternId": "U", "rotation": 180}, "RIGHT": {"patternId": "circle", "rotation": 180}}, "bottom_faces": [{"patternId": "A", "rotation": 180, "x": 4, "y": 2}, {"patternId": "triangle", "rotation": 90, "x": 4, "y": 1}, {"patternId": "U", "rotation": 0, "x": 3, "y": 1}, {"patternId": "A", "rotation": 90, "x": 3, "y": 2}, {"patternId": "C", "rotation": 90, "x": 2, "y": 2}, {"patternId": "circle", "rotation": 90, "x": 2, "y": 3}, {"patternId": "triangle", "rotation": 180, "x": 2, "y": 4}, {"patternId": "9", "rotation": 180, "x": 1, "y": 4}], "slot_sequence": ["BACK", "LEFT", "BOTTOM", "FRONT", "RIGHT", "BACK", "TOP"], "required_slots": ["BACK", "LEFT", "BOTTOM", "FRONT", "RIGHT", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "9", "rotation": 90}, "BOTTOM": {"patternId": "A", "rotation": 180}, "FRONT": {"patternId": "C", "rotation": 180}, "BACK": {"patternId": "triangle", "rotation": 90}, "LEFT": {"patternId": "U", "rotation": 270}, "RIGHT": {"patternId": "circle", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "9", "rotation": 90}, "BOTTOM": {"patternId": "A", "rotation": 180}, "FRONT": {"patternId": "C", "rotation": 180}, "BACK": {"patternId": "triangle", "rotation": 90}, "LEFT": {"patternId": "U", "rotation": 270}, "RIGHT": {"patternId": "circle", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C260\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> S -> W -> S -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=triangle, rotation=90, flipVertical=true\n- step 2: patternId=U, rotation=0, flipVertical=true\n- step 3: patternId=A, rotation=90, flipVertical=true\n- step 4: patternId=C, rotation=90, flipVertical=true\n- step 5: patternId=circle, rotation=90, flipVertical=true\n- step 6: patternId=triangle, rotation=180, flipVertical=true\n- step 7: patternId=9, rotation=180, flipVertical=true\n- allowed patternId values for this task: triangle, U, A, C, circle, 9, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C260"} +{"sample_id": "C261", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> W -> N -> W -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "W", "N", "W", "W", "W"], "observed_path_faces": [{"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C261_path_sequence.png"}, "metadata": {"level_id": 261, "name": "Reconstruct 261", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-261.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_up", "I", "T", "5", "L", "J"], "start_x": 5, "start_y": 1, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "arrow_up", "rotation": 270}, "BOTTOM": {"patternId": "J", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 90}, "BACK": {"patternId": "5", "rotation": 270}, "LEFT": {"patternId": "L", "rotation": 180}, "RIGHT": {"patternId": "T", "rotation": 270}}, "bottom_faces": [{"patternId": "J", "rotation": 0, "x": 5, "y": 1}, {"patternId": "I", "rotation": 90, "x": 5, "y": 2}, {"patternId": "arrow_up", "rotation": 270, "x": 5, "y": 3}, {"patternId": "L", "rotation": 270, "x": 4, "y": 3}, {"patternId": "I", "rotation": 180, "x": 4, "y": 2}, {"patternId": "J", "rotation": 90, "x": 3, "y": 2}, {"patternId": "5", "rotation": 180, "x": 2, "y": 2}, {"patternId": "arrow_up", "rotation": 0, "x": 1, "y": 2}], "slot_sequence": ["FRONT", "TOP", "LEFT", "FRONT", "BOTTOM", "BACK", "TOP"], "required_slots": ["FRONT", "TOP", "LEFT", "BOTTOM", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "arrow_up", "rotation": 270}, "BOTTOM": {"patternId": "J", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 90}, "BACK": {"patternId": "5", "rotation": 90}, "LEFT": {"patternId": "L", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "arrow_up", "rotation": 270}, "BOTTOM": {"patternId": "J", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 90}, "BACK": {"patternId": "5", "rotation": 90}, "LEFT": {"patternId": "L", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C261\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> W -> N -> W -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=I, rotation=90, flipVertical=true\n- step 2: patternId=arrow_up, rotation=270, flipVertical=true\n- step 3: patternId=L, rotation=270, flipVertical=true\n- step 4: patternId=I, rotation=180, flipVertical=true\n- step 5: patternId=J, rotation=90, flipVertical=true\n- step 6: patternId=5, rotation=180, flipVertical=true\n- step 7: patternId=arrow_up, rotation=0, flipVertical=true\n- allowed patternId values for this task: I, arrow_up, L, J, 5, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C261"} +{"sample_id": "C262", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> S -> E -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "W", "S", "E", "W", "S"], "observed_path_faces": [{"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C262_path_sequence.png"}, "metadata": {"level_id": 262, "name": "Reconstruct 262", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-262.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["8", "I", "M", "5", "star", "3"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "8", "rotation": 90}, "BOTTOM": {"patternId": "3", "rotation": 90}, "FRONT": {"patternId": "I", "rotation": 90}, "BACK": {"patternId": "5", "rotation": 270}, "LEFT": {"patternId": "star", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 270}}, "bottom_faces": [{"patternId": "3", "rotation": 90, "x": 1, "y": 1}, {"patternId": "M", "rotation": 0, "x": 2, "y": 1}, {"patternId": "I", "rotation": 180, "x": 2, "y": 2}, {"patternId": "3", "rotation": 180, "x": 1, "y": 2}, {"patternId": "star", "rotation": 0, "x": 1, "y": 3}, {"patternId": "I", "rotation": 90, "x": 2, "y": 3}, {"patternId": "star", "rotation": 0, "x": 1, "y": 3}, {"patternId": "8", "rotation": 0, "x": 1, "y": 4}], "slot_sequence": ["RIGHT", "FRONT", "BOTTOM", "LEFT", "FRONT", "LEFT", "TOP"], "required_slots": ["RIGHT", "FRONT", "BOTTOM", "LEFT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "8", "rotation": 90}, "BOTTOM": {"patternId": "3", "rotation": 90}, "FRONT": {"patternId": "I", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 90}, "RIGHT": {"patternId": "M", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "8", "rotation": 90}, "BOTTOM": {"patternId": "3", "rotation": 90}, "FRONT": {"patternId": "I", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 90}, "RIGHT": {"patternId": "M", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C262\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> S -> E -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=M, rotation=0, flipVertical=true\n- step 2: patternId=I, rotation=180, flipVertical=true\n- step 3: patternId=3, rotation=180, flipVertical=true\n- step 4: patternId=star, rotation=0, flipVertical=true\n- step 5: patternId=I, rotation=90, flipVertical=true\n- step 6: patternId=star, rotation=0, flipVertical=true\n- step 7: patternId=8, rotation=0, flipVertical=true\n- allowed patternId values for this task: M, I, 3, star, 8, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C262"} +{"sample_id": "C263", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> N -> E -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "N", "E", "N", "E"], "observed_path_faces": [{"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C263_path_sequence.png"}, "metadata": {"level_id": 263, "name": "Reconstruct 263", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-263.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["heart", "9", "6", "R", "heart", "K"], "start_x": 2, "start_y": 2, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "heart", "rotation": 180}, "BOTTOM": {"patternId": "K", "rotation": 180}, "FRONT": {"patternId": "9", "rotation": 180}, "BACK": {"patternId": "R", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 90}, "RIGHT": {"patternId": "6", "rotation": 90}}, "bottom_faces": [{"patternId": "K", "rotation": 180, "x": 2, "y": 2}, {"patternId": "9", "rotation": 180, "x": 2, "y": 3}, {"patternId": "heart", "rotation": 90, "x": 1, "y": 3}, {"patternId": "K", "rotation": 270, "x": 1, "y": 2}, {"patternId": "9", "rotation": 270, "x": 2, "y": 2}, {"patternId": "6", "rotation": 180, "x": 2, "y": 1}, {"patternId": "heart", "rotation": 0, "x": 3, "y": 1}], "slot_sequence": ["FRONT", "LEFT", "BOTTOM", "FRONT", "RIGHT", "TOP"], "required_slots": ["FRONT", "LEFT", "BOTTOM", "RIGHT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "heart", "rotation": 180}, "BOTTOM": {"patternId": "K", "rotation": 180}, "FRONT": {"patternId": "9", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 180}, "RIGHT": {"patternId": "6", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "heart", "rotation": 180}, "BOTTOM": {"patternId": "K", "rotation": 180}, "FRONT": {"patternId": "9", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 180}, "RIGHT": {"patternId": "6", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C263\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> N -> E -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=9, rotation=180, flipVertical=true\n- step 2: patternId=heart, rotation=90, flipVertical=true\n- step 3: patternId=K, rotation=270, flipVertical=true\n- step 4: patternId=9, rotation=270, flipVertical=true\n- step 5: patternId=6, rotation=180, flipVertical=true\n- step 6: patternId=heart, rotation=0, flipVertical=true\n- allowed patternId values for this task: 9, heart, K, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C263"} +{"sample_id": "C264", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> S -> N -> N -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "S", "N", "N", "N", "W"], "observed_path_faces": [{"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C264_path_sequence.png"}, "metadata": {"level_id": 264, "name": "Reconstruct 264", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-264.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["plus", "E", "R", "R", "R", "arrow_up"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "plus", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "E", "rotation": 180}, "BACK": {"patternId": "R", "rotation": 90}, "LEFT": {"patternId": "R", "rotation": 90}, "RIGHT": {"patternId": "R", "rotation": 0}}, "bottom_faces": [{"patternId": "arrow_up", "rotation": 270, "x": 1, "y": 2}, {"patternId": "R", "rotation": 90, "x": 2, "y": 2}, {"patternId": "E", "rotation": 270, "x": 2, "y": 3}, {"patternId": "R", "rotation": 180, "x": 2, "y": 4}, {"patternId": "E", "rotation": 270, "x": 2, "y": 3}, {"patternId": "R", "rotation": 90, "x": 2, "y": 2}, {"patternId": "R", "rotation": 180, "x": 2, "y": 1}, {"patternId": "arrow_up", "rotation": 180, "x": 1, "y": 1}], "slot_sequence": ["RIGHT", "FRONT", "LEFT", "FRONT", "RIGHT", "BACK", "BOTTOM"], "required_slots": ["RIGHT", "FRONT", "LEFT", "BACK", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "E", "rotation": 180}, "BACK": {"patternId": "R", "rotation": 270}, "LEFT": {"patternId": "R", "rotation": 180}, "RIGHT": {"patternId": "R", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "E", "rotation": 180}, "BACK": {"patternId": "R", "rotation": 270}, "LEFT": {"patternId": "R", "rotation": 180}, "RIGHT": {"patternId": "R", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C264\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> S -> N -> N -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=R, rotation=90, flipVertical=true\n- step 2: patternId=E, rotation=270, flipVertical=true\n- step 3: patternId=R, rotation=180, flipVertical=true\n- step 4: patternId=E, rotation=270, flipVertical=true\n- step 5: patternId=R, rotation=90, flipVertical=true\n- step 6: patternId=R, rotation=180, flipVertical=true\n- step 7: patternId=arrow_up, rotation=180, flipVertical=true\n- allowed patternId values for this task: R, E, arrow_up, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C264"} +{"sample_id": "C265", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> W -> S -> E -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "W", "S", "E", "S", "E"], "observed_path_faces": [{"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C265_path_sequence.png"}, "metadata": {"level_id": 265, "name": "Reconstruct 265", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-265.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["P", "Q", "arrow_up", "6", "Q", "Y"], "start_x": 3, "start_y": 2, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "P", "rotation": 180}, "BOTTOM": {"patternId": "Y", "rotation": 90}, "FRONT": {"patternId": "Q", "rotation": 90}, "BACK": {"patternId": "6", "rotation": 180}, "LEFT": {"patternId": "Q", "rotation": 90}, "RIGHT": {"patternId": "arrow_up", "rotation": 0}}, "bottom_faces": [{"patternId": "Y", "rotation": 90, "x": 3, "y": 2}, {"patternId": "Q", "rotation": 0, "x": 2, "y": 2}, {"patternId": "6", "rotation": 90, "x": 2, "y": 1}, {"patternId": "P", "rotation": 270, "x": 1, "y": 1}, {"patternId": "Q", "rotation": 270, "x": 1, "y": 2}, {"patternId": "6", "rotation": 0, "x": 2, "y": 2}, {"patternId": "Y", "rotation": 90, "x": 2, "y": 3}, {"patternId": "arrow_up", "rotation": 90, "x": 3, "y": 3}], "slot_sequence": ["LEFT", "BACK", "TOP", "LEFT", "BACK", "BOTTOM", "RIGHT"], "required_slots": ["LEFT", "BACK", "TOP", "BOTTOM", "RIGHT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "P", "rotation": 180}, "BOTTOM": {"patternId": "Y", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "Q", "rotation": 180}, "RIGHT": {"patternId": "arrow_up", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "P", "rotation": 180}, "BOTTOM": {"patternId": "Y", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "Q", "rotation": 180}, "RIGHT": {"patternId": "arrow_up", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C265\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> W -> S -> E -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Q, rotation=0, flipVertical=true\n- step 2: patternId=6, rotation=90, flipVertical=true\n- step 3: patternId=P, rotation=270, flipVertical=true\n- step 4: patternId=Q, rotation=270, flipVertical=true\n- step 5: patternId=6, rotation=0, flipVertical=true\n- step 6: patternId=Y, rotation=90, flipVertical=true\n- step 7: patternId=arrow_up, rotation=90, flipVertical=true\n- allowed patternId values for this task: Q, 6, P, Y, arrow_up, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C265"} +{"sample_id": "C266", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> S -> S -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "S", "S", "N", "N"], "observed_path_faces": [{"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C266_path_sequence.png"}, "metadata": {"level_id": 266, "name": "Reconstruct 266", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-266.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["A", "4", "N", "star", "R", "circle"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "A", "rotation": 180}, "BOTTOM": {"patternId": "circle", "rotation": 0}, "FRONT": {"patternId": "4", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 0}, "RIGHT": {"patternId": "N", "rotation": 90}}, "bottom_faces": [{"patternId": "circle", "rotation": 0, "x": 3, "y": 1}, {"patternId": "R", "rotation": 270, "x": 2, "y": 1}, {"patternId": "A", "rotation": 0, "x": 1, "y": 1}, {"patternId": "4", "rotation": 180, "x": 1, "y": 2}, {"patternId": "circle", "rotation": 180, "x": 1, "y": 3}, {"patternId": "4", "rotation": 180, "x": 1, "y": 2}, {"patternId": "A", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "TOP", "FRONT", "BOTTOM", "FRONT", "TOP"], "required_slots": ["LEFT", "TOP", "FRONT", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "A", "rotation": 180}, "BOTTOM": {"patternId": "circle", "rotation": 0}, "FRONT": {"patternId": "4", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "A", "rotation": 180}, "BOTTOM": {"patternId": "circle", "rotation": 0}, "FRONT": {"patternId": "4", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C266\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> S -> S -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=R, rotation=270, flipVertical=true\n- step 2: patternId=A, rotation=0, flipVertical=true\n- step 3: patternId=4, rotation=180, flipVertical=true\n- step 4: patternId=circle, rotation=180, flipVertical=true\n- step 5: patternId=4, rotation=180, flipVertical=true\n- step 6: patternId=A, rotation=0, flipVertical=true\n- allowed patternId values for this task: R, A, 4, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C266"} +{"sample_id": "C267", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> S -> S -> E -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "S", "S", "E", "S", "S"], "observed_path_faces": [{"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C267_path_sequence.png"}, "metadata": {"level_id": 267, "name": "Reconstruct 267", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-267.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["M", "3", "Z", "V", "J", "6"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "M", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 90}, "FRONT": {"patternId": "3", "rotation": 270}, "BACK": {"patternId": "V", "rotation": 90}, "LEFT": {"patternId": "J", "rotation": 90}, "RIGHT": {"patternId": "Z", "rotation": 0}}, "bottom_faces": [{"patternId": "6", "rotation": 90, "x": 2, "y": 1}, {"patternId": "3", "rotation": 270, "x": 2, "y": 2}, {"patternId": "J", "rotation": 90, "x": 1, "y": 2}, {"patternId": "M", "rotation": 270, "x": 1, "y": 3}, {"patternId": "Z", "rotation": 180, "x": 1, "y": 4}, {"patternId": "3", "rotation": 90, "x": 2, "y": 4}, {"patternId": "6", "rotation": 270, "x": 2, "y": 5}, {"patternId": "V", "rotation": 90, "x": 2, "y": 6}], "slot_sequence": ["FRONT", "LEFT", "TOP", "RIGHT", "FRONT", "BOTTOM", "BACK"], "required_slots": ["FRONT", "LEFT", "TOP", "RIGHT", "BOTTOM", "BACK"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "M", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 90}, "FRONT": {"patternId": "3", "rotation": 270}, "BACK": {"patternId": "V", "rotation": 270}, "LEFT": {"patternId": "J", "rotation": 180}, "RIGHT": {"patternId": "Z", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 90}, "FRONT": {"patternId": "3", "rotation": 270}, "BACK": {"patternId": "V", "rotation": 270}, "LEFT": {"patternId": "J", "rotation": 180}, "RIGHT": {"patternId": "Z", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C267\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> S -> S -> E -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=3, rotation=270, flipVertical=true\n- step 2: patternId=J, rotation=90, flipVertical=true\n- step 3: patternId=M, rotation=270, flipVertical=true\n- step 4: patternId=Z, rotation=180, flipVertical=true\n- step 5: patternId=3, rotation=90, flipVertical=true\n- step 6: patternId=6, rotation=270, flipVertical=true\n- step 7: patternId=V, rotation=90, flipVertical=true\n- allowed patternId values for this task: 3, J, M, Z, 6, V, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C267"} +{"sample_id": "C268", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> N -> N -> W -> W -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "N", "N", "W", "W", "S", "S"], "observed_path_faces": [{"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C268_path_sequence.png"}, "metadata": {"level_id": 268, "name": "Reconstruct 268", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-268.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["P", "arrow_down", "8", "diamond", "Y", "9"], "start_x": 3, "start_y": 2, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "P", "rotation": 270}, "BOTTOM": {"patternId": "9", "rotation": 180}, "FRONT": {"patternId": "arrow_down", "rotation": 90}, "BACK": {"patternId": "diamond", "rotation": 180}, "LEFT": {"patternId": "Y", "rotation": 270}, "RIGHT": {"patternId": "8", "rotation": 90}}, "bottom_faces": [{"patternId": "9", "rotation": 180, "x": 3, "y": 2}, {"patternId": "arrow_down", "rotation": 90, "x": 3, "y": 3}, {"patternId": "9", "rotation": 180, "x": 3, "y": 2}, {"patternId": "diamond", "rotation": 0, "x": 3, "y": 1}, {"patternId": "Y", "rotation": 90, "x": 2, "y": 1}, {"patternId": "arrow_down", "rotation": 270, "x": 1, "y": 1}, {"patternId": "9", "rotation": 0, "x": 1, "y": 2}, {"patternId": "diamond", "rotation": 180, "x": 1, "y": 3}], "slot_sequence": ["FRONT", "BOTTOM", "BACK", "LEFT", "FRONT", "BOTTOM", "BACK"], "required_slots": ["FRONT", "BOTTOM", "BACK", "LEFT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "9", "rotation": 180}, "FRONT": {"patternId": "arrow_down", "rotation": 90}, "BACK": {"patternId": "diamond", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "9", "rotation": 180}, "FRONT": {"patternId": "arrow_down", "rotation": 90}, "BACK": {"patternId": "diamond", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C268\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): S -> N -> N -> W -> W -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_down, rotation=90, flipVertical=true\n- step 2: patternId=9, rotation=180, flipVertical=true\n- step 3: patternId=diamond, rotation=0, flipVertical=true\n- step 4: patternId=Y, rotation=90, flipVertical=true\n- step 5: patternId=arrow_down, rotation=270, flipVertical=true\n- step 6: patternId=9, rotation=0, flipVertical=true\n- step 7: patternId=diamond, rotation=180, flipVertical=true\n- allowed patternId values for this task: arrow_down, 9, diamond, Y, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C268"} +{"sample_id": "C269", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> N -> N -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "N", "N", "N", "W"], "observed_path_faces": [{"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C269_path_sequence.png"}, "metadata": {"level_id": 269, "name": "Reconstruct 269", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-269.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["C", "Y", "arrow_up", "square", "arrow_up", "F"], "start_x": 3, "start_y": 5, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "C", "rotation": 270}, "BOTTOM": {"patternId": "F", "rotation": 90}, "FRONT": {"patternId": "Y", "rotation": 90}, "BACK": {"patternId": "square", "rotation": 0}, "LEFT": {"patternId": "arrow_up", "rotation": 0}, "RIGHT": {"patternId": "arrow_up", "rotation": 0}}, "bottom_faces": [{"patternId": "F", "rotation": 90, "x": 3, "y": 5}, {"patternId": "square", "rotation": 180, "x": 3, "y": 4}, {"patternId": "arrow_up", "rotation": 180, "x": 2, "y": 4}, {"patternId": "C", "rotation": 0, "x": 2, "y": 3}, {"patternId": "arrow_up", "rotation": 0, "x": 2, "y": 2}, {"patternId": "F", "rotation": 0, "x": 2, "y": 1}, {"patternId": "Y", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["BACK", "LEFT", "TOP", "RIGHT", "BOTTOM", "FRONT"], "required_slots": ["BACK", "LEFT", "TOP", "RIGHT", "BOTTOM", "FRONT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "C", "rotation": 270}, "BOTTOM": {"patternId": "F", "rotation": 90}, "FRONT": {"patternId": "Y", "rotation": 90}, "BACK": {"patternId": "square", "rotation": 180}, "LEFT": {"patternId": "arrow_up", "rotation": 90}, "RIGHT": {"patternId": "arrow_up", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "C", "rotation": 270}, "BOTTOM": {"patternId": "F", "rotation": 90}, "FRONT": {"patternId": "Y", "rotation": 90}, "BACK": {"patternId": "square", "rotation": 180}, "LEFT": {"patternId": "arrow_up", "rotation": 90}, "RIGHT": {"patternId": "arrow_up", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C269\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> N -> N -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=square, rotation=180, flipVertical=true\n- step 2: patternId=arrow_up, rotation=180, flipVertical=true\n- step 3: patternId=C, rotation=0, flipVertical=true\n- step 4: patternId=arrow_up, rotation=0, flipVertical=true\n- step 5: patternId=F, rotation=0, flipVertical=true\n- step 6: patternId=Y, rotation=0, flipVertical=true\n- allowed patternId values for this task: square, arrow_up, C, F, Y, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C269"} +{"sample_id": "C270", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> W -> N -> S -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "W", "N", "S", "W", "W"], "observed_path_faces": [{"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C270_path_sequence.png"}, "metadata": {"level_id": 270, "name": "Reconstruct 270", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-270.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["J", "Y", "Z", "L", "V", "3"], "start_x": 5, "start_y": 3, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "J", "rotation": 0}, "BOTTOM": {"patternId": "3", "rotation": 180}, "FRONT": {"patternId": "Y", "rotation": 180}, "BACK": {"patternId": "L", "rotation": 180}, "LEFT": {"patternId": "V", "rotation": 180}, "RIGHT": {"patternId": "Z", "rotation": 0}}, "bottom_faces": [{"patternId": "3", "rotation": 180, "x": 5, "y": 3}, {"patternId": "V", "rotation": 90, "x": 4, "y": 3}, {"patternId": "L", "rotation": 90, "x": 4, "y": 2}, {"patternId": "J", "rotation": 90, "x": 3, "y": 2}, {"patternId": "Z", "rotation": 0, "x": 3, "y": 1}, {"patternId": "J", "rotation": 90, "x": 3, "y": 2}, {"patternId": "Y", "rotation": 270, "x": 2, "y": 2}, {"patternId": "3", "rotation": 270, "x": 1, "y": 2}], "slot_sequence": ["LEFT", "BACK", "TOP", "RIGHT", "TOP", "FRONT", "BOTTOM"], "required_slots": ["LEFT", "BACK", "TOP", "RIGHT", "FRONT", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "J", "rotation": 0}, "BOTTOM": {"patternId": "3", "rotation": 180}, "FRONT": {"patternId": "Y", "rotation": 180}, "BACK": {"patternId": "L", "rotation": 0}, "LEFT": {"patternId": "V", "rotation": 270}, "RIGHT": {"patternId": "Z", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "J", "rotation": 0}, "BOTTOM": {"patternId": "3", "rotation": 180}, "FRONT": {"patternId": "Y", "rotation": 180}, "BACK": {"patternId": "L", "rotation": 0}, "LEFT": {"patternId": "V", "rotation": 270}, "RIGHT": {"patternId": "Z", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C270\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> W -> N -> S -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=V, rotation=90, flipVertical=true\n- step 2: patternId=L, rotation=90, flipVertical=true\n- step 3: patternId=J, rotation=90, flipVertical=true\n- step 4: patternId=Z, rotation=0, flipVertical=true\n- step 5: patternId=J, rotation=90, flipVertical=true\n- step 6: patternId=Y, rotation=270, flipVertical=true\n- step 7: patternId=3, rotation=270, flipVertical=true\n- allowed patternId values for this task: V, L, J, Z, Y, 3, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C270"} +{"sample_id": "C271", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> N -> W -> W -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "N", "W", "W", "S", "W"], "observed_path_faces": [{"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C271_path_sequence.png"}, "metadata": {"level_id": 271, "name": "Reconstruct 271", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-271.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["heart", "smile", "5", "square", "9", "square"], "start_x": 4, "start_y": 4, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "heart", "rotation": 90}, "BOTTOM": {"patternId": "square", "rotation": 0}, "FRONT": {"patternId": "smile", "rotation": 270}, "BACK": {"patternId": "square", "rotation": 270}, "LEFT": {"patternId": "9", "rotation": 180}, "RIGHT": {"patternId": "5", "rotation": 90}}, "bottom_faces": [{"patternId": "square", "rotation": 0, "x": 4, "y": 4}, {"patternId": "square", "rotation": 90, "x": 4, "y": 3}, {"patternId": "heart", "rotation": 90, "x": 4, "y": 2}, {"patternId": "smile", "rotation": 270, "x": 4, "y": 1}, {"patternId": "9", "rotation": 180, "x": 3, "y": 1}, {"patternId": "square", "rotation": 270, "x": 2, "y": 1}, {"patternId": "heart", "rotation": 270, "x": 2, "y": 2}, {"patternId": "5", "rotation": 180, "x": 1, "y": 2}], "slot_sequence": ["BACK", "TOP", "FRONT", "LEFT", "BACK", "TOP", "RIGHT"], "required_slots": ["BACK", "TOP", "FRONT", "LEFT", "RIGHT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "heart", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "smile", "rotation": 270}, "BACK": {"patternId": "square", "rotation": 90}, "LEFT": {"patternId": "9", "rotation": 270}, "RIGHT": {"patternId": "5", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "heart", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "smile", "rotation": 270}, "BACK": {"patternId": "square", "rotation": 90}, "LEFT": {"patternId": "9", "rotation": 270}, "RIGHT": {"patternId": "5", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C271\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> N -> W -> W -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=square, rotation=90, flipVertical=true\n- step 2: patternId=heart, rotation=90, flipVertical=true\n- step 3: patternId=smile, rotation=270, flipVertical=true\n- step 4: patternId=9, rotation=180, flipVertical=true\n- step 5: patternId=square, rotation=270, flipVertical=true\n- step 6: patternId=heart, rotation=270, flipVertical=true\n- step 7: patternId=5, rotation=180, flipVertical=true\n- allowed patternId values for this task: square, heart, smile, 9, 5, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C271"} +{"sample_id": "C272", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> W -> N -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "W", "W", "N", "S", "W"], "observed_path_faces": [{"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C272_path_sequence.png"}, "metadata": {"level_id": 272, "name": "Reconstruct 272", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-272.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["F", "heart", "W", "M", "O", "A"], "start_x": 3, "start_y": 1, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "F", "rotation": 270}, "BOTTOM": {"patternId": "A", "rotation": 90}, "FRONT": {"patternId": "heart", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 270}, "RIGHT": {"patternId": "W", "rotation": 180}}, "bottom_faces": [{"patternId": "A", "rotation": 90, "x": 3, "y": 1}, {"patternId": "W", "rotation": 270, "x": 4, "y": 1}, {"patternId": "heart", "rotation": 90, "x": 4, "y": 2}, {"patternId": "A", "rotation": 180, "x": 3, "y": 2}, {"patternId": "M", "rotation": 270, "x": 2, "y": 2}, {"patternId": "W", "rotation": 90, "x": 2, "y": 1}, {"patternId": "M", "rotation": 270, "x": 2, "y": 2}, {"patternId": "F", "rotation": 0, "x": 1, "y": 2}], "slot_sequence": ["RIGHT", "FRONT", "BOTTOM", "BACK", "RIGHT", "BACK", "TOP"], "required_slots": ["RIGHT", "FRONT", "BOTTOM", "BACK", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "F", "rotation": 270}, "BOTTOM": {"patternId": "A", "rotation": 90}, "FRONT": {"patternId": "heart", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "W", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "F", "rotation": 270}, "BOTTOM": {"patternId": "A", "rotation": 90}, "FRONT": {"patternId": "heart", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "W", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C272\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> W -> N -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=W, rotation=270, flipVertical=true\n- step 2: patternId=heart, rotation=90, flipVertical=true\n- step 3: patternId=A, rotation=180, flipVertical=true\n- step 4: patternId=M, rotation=270, flipVertical=true\n- step 5: patternId=W, rotation=90, flipVertical=true\n- step 6: patternId=M, rotation=270, flipVertical=true\n- step 7: patternId=F, rotation=0, flipVertical=true\n- allowed patternId values for this task: W, heart, A, M, F, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C272"} +{"sample_id": "C273", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> S -> E -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "S", "E", "W", "N"], "observed_path_faces": [{"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C273_path_sequence.png"}, "metadata": {"level_id": 273, "name": "Reconstruct 273", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-273.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["1", "D", "arrow_right", "D", "B", "circle"], "start_x": 1, "start_y": 2, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "1", "rotation": 0}, "BOTTOM": {"patternId": "circle", "rotation": 180}, "FRONT": {"patternId": "D", "rotation": 270}, "BACK": {"patternId": "D", "rotation": 180}, "LEFT": {"patternId": "B", "rotation": 90}, "RIGHT": {"patternId": "arrow_right", "rotation": 90}}, "bottom_faces": [{"patternId": "circle", "rotation": 180, "x": 1, "y": 2}, {"patternId": "D", "rotation": 0, "x": 1, "y": 1}, {"patternId": "arrow_right", "rotation": 270, "x": 2, "y": 1}, {"patternId": "circle", "rotation": 270, "x": 2, "y": 2}, {"patternId": "D", "rotation": 0, "x": 3, "y": 2}, {"patternId": "circle", "rotation": 270, "x": 2, "y": 2}, {"patternId": "arrow_right", "rotation": 270, "x": 2, "y": 1}], "slot_sequence": ["BACK", "RIGHT", "BOTTOM", "FRONT", "BOTTOM", "RIGHT"], "required_slots": ["BACK", "RIGHT", "BOTTOM", "FRONT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "circle", "rotation": 180}, "FRONT": {"patternId": "D", "rotation": 270}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "circle", "rotation": 180}, "FRONT": {"patternId": "D", "rotation": 270}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C273\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> S -> E -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=D, rotation=0, flipVertical=true\n- step 2: patternId=arrow_right, rotation=270, flipVertical=true\n- step 3: patternId=circle, rotation=270, flipVertical=true\n- step 4: patternId=D, rotation=0, flipVertical=true\n- step 5: patternId=circle, rotation=270, flipVertical=true\n- step 6: patternId=arrow_right, rotation=270, flipVertical=true\n- allowed patternId values for this task: D, arrow_right, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C273"} +{"sample_id": "C274", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> W -> N -> N -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "W", "N", "N", "E", "N"], "observed_path_faces": [{"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C274_path_sequence.png"}, "metadata": {"level_id": 274, "name": "Reconstruct 274", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-274.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_left", "Y", "Y", "9", "B", "7"], "start_x": 3, "start_y": 5, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "arrow_left", "rotation": 0}, "BOTTOM": {"patternId": "7", "rotation": 180}, "FRONT": {"patternId": "Y", "rotation": 180}, "BACK": {"patternId": "9", "rotation": 270}, "LEFT": {"patternId": "B", "rotation": 270}, "RIGHT": {"patternId": "Y", "rotation": 180}}, "bottom_faces": [{"patternId": "7", "rotation": 180, "x": 3, "y": 5}, {"patternId": "B", "rotation": 180, "x": 2, "y": 5}, {"patternId": "9", "rotation": 180, "x": 2, "y": 4}, {"patternId": "arrow_left", "rotation": 90, "x": 1, "y": 4}, {"patternId": "Y", "rotation": 180, "x": 1, "y": 3}, {"patternId": "7", "rotation": 90, "x": 1, "y": 2}, {"patternId": "9", "rotation": 0, "x": 2, "y": 2}, {"patternId": "B", "rotation": 0, "x": 2, "y": 1}], "slot_sequence": ["LEFT", "BACK", "TOP", "RIGHT", "BOTTOM", "BACK", "LEFT"], "required_slots": ["LEFT", "BACK", "TOP", "RIGHT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "arrow_left", "rotation": 0}, "BOTTOM": {"patternId": "7", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "9", "rotation": 90}, "LEFT": {"patternId": "B", "rotation": 0}, "RIGHT": {"patternId": "Y", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "arrow_left", "rotation": 0}, "BOTTOM": {"patternId": "7", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "9", "rotation": 90}, "LEFT": {"patternId": "B", "rotation": 0}, "RIGHT": {"patternId": "Y", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C274\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> W -> N -> N -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=B, rotation=180, flipVertical=true\n- step 2: patternId=9, rotation=180, flipVertical=true\n- step 3: patternId=arrow_left, rotation=90, flipVertical=true\n- step 4: patternId=Y, rotation=180, flipVertical=true\n- step 5: patternId=7, rotation=90, flipVertical=true\n- step 6: patternId=9, rotation=0, flipVertical=true\n- step 7: patternId=B, rotation=0, flipVertical=true\n- allowed patternId values for this task: B, 9, arrow_left, Y, 7, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C274"} +{"sample_id": "C275", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> S -> W -> W -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "S", "W", "W", "S", "S"], "observed_path_faces": [{"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C275_path_sequence.png"}, "metadata": {"level_id": 275, "name": "Reconstruct 275", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-275.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["6", "O", "smile", "I", "arrow_down", "arrow_up"], "start_x": 3, "start_y": 3, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "6", "rotation": 180}, "BOTTOM": {"patternId": "arrow_up", "rotation": 180}, "FRONT": {"patternId": "O", "rotation": 270}, "BACK": {"patternId": "I", "rotation": 90}, "LEFT": {"patternId": "arrow_down", "rotation": 90}, "RIGHT": {"patternId": "smile", "rotation": 270}}, "bottom_faces": [{"patternId": "arrow_up", "rotation": 180, "x": 3, "y": 3}, {"patternId": "I", "rotation": 270, "x": 3, "y": 2}, {"patternId": "6", "rotation": 180, "x": 3, "y": 1}, {"patternId": "I", "rotation": 270, "x": 3, "y": 2}, {"patternId": "arrow_down", "rotation": 270, "x": 2, "y": 2}, {"patternId": "O", "rotation": 90, "x": 1, "y": 2}, {"patternId": "arrow_up", "rotation": 0, "x": 1, "y": 3}, {"patternId": "I", "rotation": 90, "x": 1, "y": 4}], "slot_sequence": ["BACK", "TOP", "BACK", "LEFT", "FRONT", "BOTTOM", "BACK"], "required_slots": ["BACK", "TOP", "LEFT", "FRONT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "6", "rotation": 180}, "BOTTOM": {"patternId": "arrow_up", "rotation": 180}, "FRONT": {"patternId": "O", "rotation": 270}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "arrow_down", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 180}, "BOTTOM": {"patternId": "arrow_up", "rotation": 180}, "FRONT": {"patternId": "O", "rotation": 270}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "arrow_down", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C275\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> S -> W -> W -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=I, rotation=270, flipVertical=true\n- step 2: patternId=6, rotation=180, flipVertical=true\n- step 3: patternId=I, rotation=270, flipVertical=true\n- step 4: patternId=arrow_down, rotation=270, flipVertical=true\n- step 5: patternId=O, rotation=90, flipVertical=true\n- step 6: patternId=arrow_up, rotation=0, flipVertical=true\n- step 7: patternId=I, rotation=90, flipVertical=true\n- allowed patternId values for this task: I, 6, arrow_down, O, arrow_up, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C275"} +{"sample_id": "C276", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> E -> S -> E -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "E", "S", "E", "E", "E"], "observed_path_faces": [{"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C276_path_sequence.png"}, "metadata": {"level_id": 276, "name": "Reconstruct 276", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-276.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["R", "B", "S", "arrow_left", "circle", "C"], "start_x": 1, "start_y": 1, "grid_width": 8, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "R", "rotation": 180}, "BOTTOM": {"patternId": "C", "rotation": 180}, "FRONT": {"patternId": "B", "rotation": 270}, "BACK": {"patternId": "arrow_left", "rotation": 180}, "LEFT": {"patternId": "circle", "rotation": 180}, "RIGHT": {"patternId": "S", "rotation": 90}}, "bottom_faces": [{"patternId": "C", "rotation": 180, "x": 1, "y": 1}, {"patternId": "S", "rotation": 180, "x": 2, "y": 1}, {"patternId": "B", "rotation": 0, "x": 2, "y": 2}, {"patternId": "R", "rotation": 270, "x": 3, "y": 2}, {"patternId": "circle", "rotation": 0, "x": 3, "y": 3}, {"patternId": "arrow_left", "rotation": 0, "x": 4, "y": 3}, {"patternId": "S", "rotation": 270, "x": 5, "y": 3}, {"patternId": "B", "rotation": 90, "x": 6, "y": 3}], "slot_sequence": ["RIGHT", "FRONT", "TOP", "LEFT", "BACK", "RIGHT", "FRONT"], "required_slots": ["RIGHT", "FRONT", "TOP", "LEFT", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "R", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 270}, "BACK": {"patternId": "arrow_left", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 270}, "RIGHT": {"patternId": "S", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "R", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 270}, "BACK": {"patternId": "arrow_left", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 270}, "RIGHT": {"patternId": "S", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C276\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> E -> S -> E -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=S, rotation=180, flipVertical=true\n- step 2: patternId=B, rotation=0, flipVertical=true\n- step 3: patternId=R, rotation=270, flipVertical=true\n- step 4: patternId=circle, rotation=0, flipVertical=true\n- step 5: patternId=arrow_left, rotation=0, flipVertical=true\n- step 6: patternId=S, rotation=270, flipVertical=true\n- step 7: patternId=B, rotation=90, flipVertical=true\n- allowed patternId values for this task: S, B, R, circle, arrow_left, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C276"} +{"sample_id": "C277", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> S -> E -> N -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "S", "E", "N", "W", "N"], "observed_path_faces": [{"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C277_path_sequence.png"}, "metadata": {"level_id": 277, "name": "Reconstruct 277", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-277.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_up", "7", "C", "R", "2", "K"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "arrow_up", "rotation": 270}, "BOTTOM": {"patternId": "K", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 270}, "LEFT": {"patternId": "2", "rotation": 180}, "RIGHT": {"patternId": "C", "rotation": 270}}, "bottom_faces": [{"patternId": "K", "rotation": 0, "x": 2, "y": 1}, {"patternId": "7", "rotation": 0, "x": 2, "y": 2}, {"patternId": "2", "rotation": 180, "x": 1, "y": 2}, {"patternId": "arrow_up", "rotation": 180, "x": 1, "y": 3}, {"patternId": "7", "rotation": 270, "x": 2, "y": 3}, {"patternId": "2", "rotation": 90, "x": 2, "y": 2}, {"patternId": "arrow_up", "rotation": 90, "x": 1, "y": 2}, {"patternId": "R", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["FRONT", "LEFT", "TOP", "FRONT", "LEFT", "TOP", "BACK"], "required_slots": ["FRONT", "LEFT", "TOP", "BACK"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "arrow_up", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 90}, "LEFT": {"patternId": "2", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "arrow_up", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 90}, "LEFT": {"patternId": "2", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C277\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> S -> E -> N -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=7, rotation=0, flipVertical=true\n- step 2: patternId=2, rotation=180, flipVertical=true\n- step 3: patternId=arrow_up, rotation=180, flipVertical=true\n- step 4: patternId=7, rotation=270, flipVertical=true\n- step 5: patternId=2, rotation=90, flipVertical=true\n- step 6: patternId=arrow_up, rotation=90, flipVertical=true\n- step 7: patternId=R, rotation=270, flipVertical=true\n- allowed patternId values for this task: 7, 2, arrow_up, R, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C277"} +{"sample_id": "C278", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> E -> N -> S -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "E", "N", "S", "N", "N"], "observed_path_faces": [{"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C278_path_sequence.png"}, "metadata": {"level_id": 278, "name": "Reconstruct 278", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-278.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["B", "H", "U", "D", "A", "6"], "start_x": 2, "start_y": 3, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "B", "rotation": 270}, "BOTTOM": {"patternId": "6", "rotation": 270}, "FRONT": {"patternId": "H", "rotation": 180}, "BACK": {"patternId": "D", "rotation": 90}, "LEFT": {"patternId": "A", "rotation": 90}, "RIGHT": {"patternId": "U", "rotation": 90}}, "bottom_faces": [{"patternId": "6", "rotation": 270, "x": 2, "y": 3}, {"patternId": "A", "rotation": 0, "x": 1, "y": 3}, {"patternId": "6", "rotation": 270, "x": 2, "y": 3}, {"patternId": "D", "rotation": 270, "x": 2, "y": 2}, {"patternId": "6", "rotation": 270, "x": 2, "y": 3}, {"patternId": "D", "rotation": 270, "x": 2, "y": 2}, {"patternId": "B", "rotation": 270, "x": 2, "y": 1}], "slot_sequence": ["LEFT", "BOTTOM", "BACK", "BOTTOM", "BACK", "TOP"], "required_slots": ["LEFT", "BOTTOM", "BACK", "TOP"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "B", "rotation": 270}, "BOTTOM": {"patternId": "6", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 270}, "LEFT": {"patternId": "A", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "B", "rotation": 270}, "BOTTOM": {"patternId": "6", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 270}, "LEFT": {"patternId": "A", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C278\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): W -> E -> N -> S -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=A, rotation=0, flipVertical=true\n- step 2: patternId=6, rotation=270, flipVertical=true\n- step 3: patternId=D, rotation=270, flipVertical=true\n- step 4: patternId=6, rotation=270, flipVertical=true\n- step 5: patternId=D, rotation=270, flipVertical=true\n- step 6: patternId=B, rotation=270, flipVertical=true\n- allowed patternId values for this task: A, 6, D, B, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C278"} +{"sample_id": "C279", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> W -> E -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "W", "E", "W", "S"], "observed_path_faces": [{"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C279_path_sequence.png"}, "metadata": {"level_id": 279, "name": "Reconstruct 279", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-279.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["O", "N", "arrow_up", "arrow_right", "2", "F"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "O", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 270}, "BACK": {"patternId": "arrow_right", "rotation": 270}, "LEFT": {"patternId": "2", "rotation": 90}, "RIGHT": {"patternId": "arrow_up", "rotation": 270}}, "bottom_faces": [{"patternId": "F", "rotation": 0, "x": 3, "y": 1}, {"patternId": "2", "rotation": 0, "x": 2, "y": 1}, {"patternId": "N", "rotation": 180, "x": 2, "y": 2}, {"patternId": "O", "rotation": 270, "x": 1, "y": 2}, {"patternId": "N", "rotation": 180, "x": 2, "y": 2}, {"patternId": "O", "rotation": 270, "x": 1, "y": 2}, {"patternId": "arrow_up", "rotation": 90, "x": 1, "y": 3}], "slot_sequence": ["LEFT", "FRONT", "TOP", "FRONT", "TOP", "RIGHT"], "required_slots": ["LEFT", "FRONT", "TOP", "RIGHT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "O", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "2", "rotation": 180}, "RIGHT": {"patternId": "arrow_up", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "2", "rotation": 180}, "RIGHT": {"patternId": "arrow_up", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C279\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> W -> E -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=2, rotation=0, flipVertical=true\n- step 2: patternId=N, rotation=180, flipVertical=true\n- step 3: patternId=O, rotation=270, flipVertical=true\n- step 4: patternId=N, rotation=180, flipVertical=true\n- step 5: patternId=O, rotation=270, flipVertical=true\n- step 6: patternId=arrow_up, rotation=90, flipVertical=true\n- allowed patternId values for this task: 2, N, O, arrow_up, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C279"} +{"sample_id": "C280", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> N -> N -> E -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "N", "N", "E", "S", "S"], "observed_path_faces": [{"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C280_path_sequence.png"}, "metadata": {"level_id": 280, "name": "Reconstruct 280", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-280.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["D", "5", "C", "H", "arrow_up", "U"], "start_x": 2, "start_y": 4, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "D", "rotation": 270}, "BOTTOM": {"patternId": "U", "rotation": 0}, "FRONT": {"patternId": "5", "rotation": 180}, "BACK": {"patternId": "H", "rotation": 0}, "LEFT": {"patternId": "arrow_up", "rotation": 0}, "RIGHT": {"patternId": "C", "rotation": 180}}, "bottom_faces": [{"patternId": "U", "rotation": 0, "x": 2, "y": 4}, {"patternId": "arrow_up", "rotation": 270, "x": 1, "y": 4}, {"patternId": "H", "rotation": 270, "x": 1, "y": 3}, {"patternId": "C", "rotation": 90, "x": 1, "y": 2}, {"patternId": "5", "rotation": 90, "x": 1, "y": 1}, {"patternId": "U", "rotation": 270, "x": 2, "y": 1}, {"patternId": "C", "rotation": 180, "x": 2, "y": 2}, {"patternId": "D", "rotation": 0, "x": 2, "y": 3}], "slot_sequence": ["LEFT", "BACK", "RIGHT", "FRONT", "BOTTOM", "RIGHT", "TOP"], "required_slots": ["LEFT", "BACK", "RIGHT", "FRONT", "BOTTOM", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "D", "rotation": 270}, "BOTTOM": {"patternId": "U", "rotation": 0}, "FRONT": {"patternId": "5", "rotation": 180}, "BACK": {"patternId": "H", "rotation": 180}, "LEFT": {"patternId": "arrow_up", "rotation": 90}, "RIGHT": {"patternId": "C", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "D", "rotation": 270}, "BOTTOM": {"patternId": "U", "rotation": 0}, "FRONT": {"patternId": "5", "rotation": 180}, "BACK": {"patternId": "H", "rotation": 180}, "LEFT": {"patternId": "arrow_up", "rotation": 90}, "RIGHT": {"patternId": "C", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C280\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> N -> N -> E -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_up, rotation=270, flipVertical=true\n- step 2: patternId=H, rotation=270, flipVertical=true\n- step 3: patternId=C, rotation=90, flipVertical=true\n- step 4: patternId=5, rotation=90, flipVertical=true\n- step 5: patternId=U, rotation=270, flipVertical=true\n- step 6: patternId=C, rotation=180, flipVertical=true\n- step 7: patternId=D, rotation=0, flipVertical=true\n- allowed patternId values for this task: arrow_up, H, C, 5, U, D, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C280"} +{"sample_id": "C281", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> W -> E -> E -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "W", "E", "E", "E", "N"], "observed_path_faces": [{"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C281_path_sequence.png"}, "metadata": {"level_id": 281, "name": "Reconstruct 281", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-281.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_right", "1", "J", "diamond", "C", "arrow_left"], "start_x": 4, "start_y": 2, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "arrow_right", "rotation": 90}, "BOTTOM": {"patternId": "arrow_left", "rotation": 180}, "FRONT": {"patternId": "1", "rotation": 270}, "BACK": {"patternId": "diamond", "rotation": 90}, "LEFT": {"patternId": "C", "rotation": 180}, "RIGHT": {"patternId": "J", "rotation": 270}}, "bottom_faces": [{"patternId": "arrow_left", "rotation": 180, "x": 4, "y": 2}, {"patternId": "C", "rotation": 90, "x": 3, "y": 2}, {"patternId": "arrow_right", "rotation": 270, "x": 2, "y": 2}, {"patternId": "J", "rotation": 0, "x": 1, "y": 2}, {"patternId": "arrow_right", "rotation": 270, "x": 2, "y": 2}, {"patternId": "C", "rotation": 90, "x": 3, "y": 2}, {"patternId": "arrow_left", "rotation": 180, "x": 4, "y": 2}, {"patternId": "diamond", "rotation": 270, "x": 4, "y": 1}], "slot_sequence": ["LEFT", "TOP", "RIGHT", "TOP", "LEFT", "BOTTOM", "BACK"], "required_slots": ["LEFT", "TOP", "RIGHT", "BOTTOM", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "arrow_right", "rotation": 90}, "BOTTOM": {"patternId": "arrow_left", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "diamond", "rotation": 270}, "LEFT": {"patternId": "C", "rotation": 270}, "RIGHT": {"patternId": "J", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "arrow_right", "rotation": 90}, "BOTTOM": {"patternId": "arrow_left", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "diamond", "rotation": 270}, "LEFT": {"patternId": "C", "rotation": 270}, "RIGHT": {"patternId": "J", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C281\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> W -> E -> E -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=C, rotation=90, flipVertical=true\n- step 2: patternId=arrow_right, rotation=270, flipVertical=true\n- step 3: patternId=J, rotation=0, flipVertical=true\n- step 4: patternId=arrow_right, rotation=270, flipVertical=true\n- step 5: patternId=C, rotation=90, flipVertical=true\n- step 6: patternId=arrow_left, rotation=180, flipVertical=true\n- step 7: patternId=diamond, rotation=270, flipVertical=true\n- allowed patternId values for this task: C, arrow_right, J, arrow_left, diamond, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C281"} +{"sample_id": "C282", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> E -> S -> E -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "E", "S", "E", "E", "E"], "observed_path_faces": [{"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C282_path_sequence.png"}, "metadata": {"level_id": 282, "name": "Reconstruct 282", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-282.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["7", "H", "4", "Z", "plus", "7"], "start_x": 1, "start_y": 1, "grid_width": 7, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "7", "rotation": 90}, "BOTTOM": {"patternId": "7", "rotation": 270}, "FRONT": {"patternId": "H", "rotation": 90}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "plus", "rotation": 180}, "RIGHT": {"patternId": "4", "rotation": 90}}, "bottom_faces": [{"patternId": "7", "rotation": 270, "x": 1, "y": 1}, {"patternId": "H", "rotation": 90, "x": 1, "y": 2}, {"patternId": "7", "rotation": 90, "x": 1, "y": 3}, {"patternId": "4", "rotation": 0, "x": 2, "y": 3}, {"patternId": "Z", "rotation": 0, "x": 2, "y": 4}, {"patternId": "7", "rotation": 0, "x": 3, "y": 4}, {"patternId": "H", "rotation": 180, "x": 4, "y": 4}, {"patternId": "7", "rotation": 180, "x": 5, "y": 4}], "slot_sequence": ["FRONT", "TOP", "RIGHT", "BACK", "BOTTOM", "FRONT", "TOP"], "required_slots": ["FRONT", "TOP", "RIGHT", "BACK", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "7", "rotation": 90}, "BOTTOM": {"patternId": "7", "rotation": 270}, "FRONT": {"patternId": "H", "rotation": 90}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "4", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "7", "rotation": 90}, "BOTTOM": {"patternId": "7", "rotation": 270}, "FRONT": {"patternId": "H", "rotation": 90}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "4", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C282\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> E -> S -> E -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=H, rotation=90, flipVertical=true\n- step 2: patternId=7, rotation=90, flipVertical=true\n- step 3: patternId=4, rotation=0, flipVertical=true\n- step 4: patternId=Z, rotation=0, flipVertical=true\n- step 5: patternId=7, rotation=0, flipVertical=true\n- step 6: patternId=H, rotation=180, flipVertical=true\n- step 7: patternId=7, rotation=180, flipVertical=true\n- allowed patternId values for this task: H, 7, 4, Z, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C282"} +{"sample_id": "C283", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> S -> W -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "S", "W", "N", "E"], "observed_path_faces": [{"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C283_path_sequence.png"}, "metadata": {"level_id": 283, "name": "Reconstruct 283", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-283.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["C", "Z", "triangle", "T", "A", "1"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "C", "rotation": 90}, "BOTTOM": {"patternId": "1", "rotation": 270}, "FRONT": {"patternId": "Z", "rotation": 90}, "BACK": {"patternId": "T", "rotation": 0}, "LEFT": {"patternId": "A", "rotation": 270}, "RIGHT": {"patternId": "triangle", "rotation": 0}}, "bottom_faces": [{"patternId": "1", "rotation": 270, "x": 1, "y": 1}, {"patternId": "triangle", "rotation": 90, "x": 2, "y": 1}, {"patternId": "Z", "rotation": 180, "x": 2, "y": 2}, {"patternId": "A", "rotation": 0, "x": 2, "y": 3}, {"patternId": "1", "rotation": 90, "x": 1, "y": 3}, {"patternId": "Z", "rotation": 270, "x": 1, "y": 2}, {"patternId": "A", "rotation": 90, "x": 2, "y": 2}], "slot_sequence": ["RIGHT", "FRONT", "LEFT", "BOTTOM", "FRONT", "LEFT"], "required_slots": ["RIGHT", "FRONT", "LEFT", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "1", "rotation": 270}, "FRONT": {"patternId": "Z", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "A", "rotation": 0}, "RIGHT": {"patternId": "triangle", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "1", "rotation": 270}, "FRONT": {"patternId": "Z", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "A", "rotation": 0}, "RIGHT": {"patternId": "triangle", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C283\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> S -> W -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=triangle, rotation=90, flipVertical=true\n- step 2: patternId=Z, rotation=180, flipVertical=true\n- step 3: patternId=A, rotation=0, flipVertical=true\n- step 4: patternId=1, rotation=90, flipVertical=true\n- step 5: patternId=Z, rotation=270, flipVertical=true\n- step 6: patternId=A, rotation=90, flipVertical=true\n- allowed patternId values for this task: triangle, Z, A, 1, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C283"} +{"sample_id": "C284", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> N -> N -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "N", "N", "W", "W"], "observed_path_faces": [{"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C284_path_sequence.png"}, "metadata": {"level_id": 284, "name": "Reconstruct 284", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-284.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["S", "C", "Z", "B", "4", "heart"], "start_x": 5, "start_y": 3, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "S", "rotation": 180}, "BOTTOM": {"patternId": "heart", "rotation": 270}, "FRONT": {"patternId": "C", "rotation": 270}, "BACK": {"patternId": "B", "rotation": 270}, "LEFT": {"patternId": "4", "rotation": 180}, "RIGHT": {"patternId": "Z", "rotation": 0}}, "bottom_faces": [{"patternId": "heart", "rotation": 270, "x": 5, "y": 3}, {"patternId": "4", "rotation": 90, "x": 4, "y": 3}, {"patternId": "S", "rotation": 0, "x": 3, "y": 3}, {"patternId": "B", "rotation": 270, "x": 3, "y": 2}, {"patternId": "heart", "rotation": 90, "x": 3, "y": 1}, {"patternId": "Z", "rotation": 270, "x": 2, "y": 1}, {"patternId": "S", "rotation": 180, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "TOP", "BACK", "BOTTOM", "RIGHT", "TOP"], "required_slots": ["LEFT", "TOP", "BACK", "BOTTOM", "RIGHT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "S", "rotation": 180}, "BOTTOM": {"patternId": "heart", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 90}, "LEFT": {"patternId": "4", "rotation": 270}, "RIGHT": {"patternId": "Z", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 180}, "BOTTOM": {"patternId": "heart", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 90}, "LEFT": {"patternId": "4", "rotation": 270}, "RIGHT": {"patternId": "Z", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C284\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> N -> N -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=4, rotation=90, flipVertical=true\n- step 2: patternId=S, rotation=0, flipVertical=true\n- step 3: patternId=B, rotation=270, flipVertical=true\n- step 4: patternId=heart, rotation=90, flipVertical=true\n- step 5: patternId=Z, rotation=270, flipVertical=true\n- step 6: patternId=S, rotation=180, flipVertical=true\n- allowed patternId values for this task: 4, S, B, heart, Z, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C284"} +{"sample_id": "C285", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> W -> E -> S -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "W", "E", "S", "W", "N"], "observed_path_faces": [{"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C285_path_sequence.png"}, "metadata": {"level_id": 285, "name": "Reconstruct 285", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-285.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["diamond", "6", "S", "C", "O", "arrow_right"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "diamond", "rotation": 270}, "BOTTOM": {"patternId": "arrow_right", "rotation": 270}, "FRONT": {"patternId": "6", "rotation": 90}, "BACK": {"patternId": "C", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 270}, "RIGHT": {"patternId": "S", "rotation": 180}}, "bottom_faces": [{"patternId": "arrow_right", "rotation": 270, "x": 3, "y": 1}, {"patternId": "O", "rotation": 180, "x": 2, "y": 1}, {"patternId": "6", "rotation": 0, "x": 2, "y": 2}, {"patternId": "diamond", "rotation": 180, "x": 1, "y": 2}, {"patternId": "6", "rotation": 0, "x": 2, "y": 2}, {"patternId": "S", "rotation": 90, "x": 2, "y": 3}, {"patternId": "diamond", "rotation": 270, "x": 1, "y": 3}, {"patternId": "6", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["LEFT", "FRONT", "TOP", "FRONT", "RIGHT", "TOP", "FRONT"], "required_slots": ["LEFT", "FRONT", "TOP", "RIGHT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "diamond", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "6", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "diamond", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "6", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C285\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> W -> E -> S -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=O, rotation=180, flipVertical=true\n- step 2: patternId=6, rotation=0, flipVertical=true\n- step 3: patternId=diamond, rotation=180, flipVertical=true\n- step 4: patternId=6, rotation=0, flipVertical=true\n- step 5: patternId=S, rotation=90, flipVertical=true\n- step 6: patternId=diamond, rotation=270, flipVertical=true\n- step 7: patternId=6, rotation=90, flipVertical=true\n- allowed patternId values for this task: O, 6, diamond, S, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C285"} +{"sample_id": "C286", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> W -> N -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "W", "N", "E", "E"], "observed_path_faces": [{"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C286_path_sequence.png"}, "metadata": {"level_id": 286, "name": "Reconstruct 286", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-286.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["circle", "smile", "O", "R", "3", "T"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "circle", "rotation": 90}, "BOTTOM": {"patternId": "T", "rotation": 90}, "FRONT": {"patternId": "smile", "rotation": 270}, "BACK": {"patternId": "R", "rotation": 270}, "LEFT": {"patternId": "3", "rotation": 270}, "RIGHT": {"patternId": "O", "rotation": 270}}, "bottom_faces": [{"patternId": "T", "rotation": 90, "x": 3, "y": 1}, {"patternId": "3", "rotation": 180, "x": 2, "y": 1}, {"patternId": "smile", "rotation": 180, "x": 2, "y": 2}, {"patternId": "circle", "rotation": 0, "x": 1, "y": 2}, {"patternId": "3", "rotation": 270, "x": 1, "y": 1}, {"patternId": "smile", "rotation": 270, "x": 2, "y": 1}, {"patternId": "O", "rotation": 270, "x": 3, "y": 1}], "slot_sequence": ["LEFT", "FRONT", "TOP", "LEFT", "FRONT", "RIGHT"], "required_slots": ["LEFT", "FRONT", "TOP", "RIGHT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "circle", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "smile", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "smile", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C286\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> W -> N -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=3, rotation=180, flipVertical=true\n- step 2: patternId=smile, rotation=180, flipVertical=true\n- step 3: patternId=circle, rotation=0, flipVertical=true\n- step 4: patternId=3, rotation=270, flipVertical=true\n- step 5: patternId=smile, rotation=270, flipVertical=true\n- step 6: patternId=O, rotation=270, flipVertical=true\n- allowed patternId values for this task: 3, smile, circle, O, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C286"} +{"sample_id": "C287", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> W -> E -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "W", "E", "N", "W"], "observed_path_faces": [{"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C287_path_sequence.png"}, "metadata": {"level_id": 287, "name": "Reconstruct 287", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-287.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["K", "circle", "D", "arrow_left", "I", "J"], "start_x": 3, "start_y": 3, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "K", "rotation": 270}, "BOTTOM": {"patternId": "J", "rotation": 180}, "FRONT": {"patternId": "circle", "rotation": 270}, "BACK": {"patternId": "arrow_left", "rotation": 270}, "LEFT": {"patternId": "I", "rotation": 180}, "RIGHT": {"patternId": "D", "rotation": 0}}, "bottom_faces": [{"patternId": "J", "rotation": 180, "x": 3, "y": 3}, {"patternId": "I", "rotation": 90, "x": 2, "y": 3}, {"patternId": "arrow_left", "rotation": 180, "x": 2, "y": 2}, {"patternId": "K", "rotation": 0, "x": 1, "y": 2}, {"patternId": "arrow_left", "rotation": 180, "x": 2, "y": 2}, {"patternId": "D", "rotation": 270, "x": 2, "y": 1}, {"patternId": "K", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "BACK", "TOP", "BACK", "RIGHT", "TOP"], "required_slots": ["LEFT", "BACK", "TOP", "RIGHT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "K", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 90}, "LEFT": {"patternId": "I", "rotation": 270}, "RIGHT": {"patternId": "D", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "K", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 90}, "LEFT": {"patternId": "I", "rotation": 270}, "RIGHT": {"patternId": "D", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C287\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> W -> E -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=I, rotation=90, flipVertical=true\n- step 2: patternId=arrow_left, rotation=180, flipVertical=true\n- step 3: patternId=K, rotation=0, flipVertical=true\n- step 4: patternId=arrow_left, rotation=180, flipVertical=true\n- step 5: patternId=D, rotation=270, flipVertical=true\n- step 6: patternId=K, rotation=270, flipVertical=true\n- allowed patternId values for this task: I, arrow_left, K, D, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C287"} +{"sample_id": "C288", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> E -> E -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "E", "E", "N", "N"], "observed_path_faces": [{"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C288_path_sequence.png"}, "metadata": {"level_id": 288, "name": "Reconstruct 288", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-288.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["T", "plus", "4", "9", "R", "9"], "start_x": 2, "start_y": 2, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "T", "rotation": 0}, "BOTTOM": {"patternId": "9", "rotation": 90}, "FRONT": {"patternId": "plus", "rotation": 180}, "BACK": {"patternId": "9", "rotation": 180}, "LEFT": {"patternId": "R", "rotation": 270}, "RIGHT": {"patternId": "4", "rotation": 270}}, "bottom_faces": [{"patternId": "9", "rotation": 90, "x": 2, "y": 2}, {"patternId": "R", "rotation": 180, "x": 1, "y": 2}, {"patternId": "plus", "rotation": 90, "x": 1, "y": 3}, {"patternId": "9", "rotation": 0, "x": 2, "y": 3}, {"patternId": "9", "rotation": 270, "x": 3, "y": 3}, {"patternId": "R", "rotation": 0, "x": 3, "y": 2}, {"patternId": "plus", "rotation": 270, "x": 3, "y": 1}], "slot_sequence": ["LEFT", "FRONT", "BOTTOM", "BACK", "LEFT", "FRONT"], "required_slots": ["LEFT", "FRONT", "BOTTOM", "BACK"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "9", "rotation": 90}, "FRONT": {"patternId": "plus", "rotation": 180}, "BACK": {"patternId": "9", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "9", "rotation": 90}, "FRONT": {"patternId": "plus", "rotation": 180}, "BACK": {"patternId": "9", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C288\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> E -> E -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=R, rotation=180, flipVertical=true\n- step 2: patternId=plus, rotation=90, flipVertical=true\n- step 3: patternId=9, rotation=0, flipVertical=true\n- step 4: patternId=9, rotation=270, flipVertical=true\n- step 5: patternId=R, rotation=0, flipVertical=true\n- step 6: patternId=plus, rotation=270, flipVertical=true\n- allowed patternId values for this task: R, plus, 9, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C288"} +{"sample_id": "C289", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> N -> E -> E -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "N", "E", "E", "W"], "observed_path_faces": [{"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C289_path_sequence.png"}, "metadata": {"level_id": 289, "name": "Reconstruct 289", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-289.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["E", "B", "arrow_right", "M", "Q", "arrow_up"], "start_x": 2, "start_y": 3, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "E", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 180}, "LEFT": {"patternId": "Q", "rotation": 90}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}}, "bottom_faces": [{"patternId": "arrow_up", "rotation": 0, "x": 2, "y": 3}, {"patternId": "M", "rotation": 0, "x": 2, "y": 2}, {"patternId": "Q", "rotation": 270, "x": 1, "y": 2}, {"patternId": "E", "rotation": 90, "x": 1, "y": 1}, {"patternId": "M", "rotation": 90, "x": 2, "y": 1}, {"patternId": "arrow_up", "rotation": 90, "x": 3, "y": 1}, {"patternId": "M", "rotation": 90, "x": 2, "y": 1}], "slot_sequence": ["BACK", "LEFT", "TOP", "BACK", "BOTTOM", "BACK"], "required_slots": ["BACK", "LEFT", "TOP", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "E", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "Q", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "E", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "Q", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C289\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> N -> E -> E -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=M, rotation=0, flipVertical=true\n- step 2: patternId=Q, rotation=270, flipVertical=true\n- step 3: patternId=E, rotation=90, flipVertical=true\n- step 4: patternId=M, rotation=90, flipVertical=true\n- step 5: patternId=arrow_up, rotation=90, flipVertical=true\n- step 6: patternId=M, rotation=90, flipVertical=true\n- allowed patternId values for this task: M, Q, E, arrow_up, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C289"} +{"sample_id": "C290", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> E -> S -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "E", "S", "S", "S"], "observed_path_faces": [{"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C290_path_sequence.png"}, "metadata": {"level_id": 290, "name": "Reconstruct 290", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-290.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_up", "J", "K", "P", "J", "arrow_left"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "arrow_up", "rotation": 0}, "BOTTOM": {"patternId": "arrow_left", "rotation": 180}, "FRONT": {"patternId": "J", "rotation": 90}, "BACK": {"patternId": "P", "rotation": 270}, "LEFT": {"patternId": "J", "rotation": 180}, "RIGHT": {"patternId": "K", "rotation": 90}}, "bottom_faces": [{"patternId": "arrow_left", "rotation": 180, "x": 1, "y": 1}, {"patternId": "J", "rotation": 90, "x": 1, "y": 2}, {"patternId": "arrow_up", "rotation": 0, "x": 1, "y": 3}, {"patternId": "K", "rotation": 0, "x": 2, "y": 3}, {"patternId": "P", "rotation": 180, "x": 2, "y": 4}, {"patternId": "J", "rotation": 90, "x": 2, "y": 5}, {"patternId": "J", "rotation": 0, "x": 2, "y": 6}], "slot_sequence": ["FRONT", "TOP", "RIGHT", "BACK", "LEFT", "FRONT"], "required_slots": ["FRONT", "TOP", "RIGHT", "BACK", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "arrow_up", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 90}, "BACK": {"patternId": "P", "rotation": 90}, "LEFT": {"patternId": "J", "rotation": 270}, "RIGHT": {"patternId": "K", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "arrow_up", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 90}, "BACK": {"patternId": "P", "rotation": 90}, "LEFT": {"patternId": "J", "rotation": 270}, "RIGHT": {"patternId": "K", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C290\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> E -> S -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=J, rotation=90, flipVertical=true\n- step 2: patternId=arrow_up, rotation=0, flipVertical=true\n- step 3: patternId=K, rotation=0, flipVertical=true\n- step 4: patternId=P, rotation=180, flipVertical=true\n- step 5: patternId=J, rotation=90, flipVertical=true\n- step 6: patternId=J, rotation=0, flipVertical=true\n- allowed patternId values for this task: J, arrow_up, K, P, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C290"} +{"sample_id": "C291", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> S -> S -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "S", "S", "S", "W"], "observed_path_faces": [{"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C291_path_sequence.png"}, "metadata": {"level_id": 291, "name": "Reconstruct 291", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-291.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["6", "J", "G", "plus", "C", "star"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "6", "rotation": 90}, "BOTTOM": {"patternId": "star", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 90}, "BACK": {"patternId": "plus", "rotation": 270}, "LEFT": {"patternId": "C", "rotation": 270}, "RIGHT": {"patternId": "G", "rotation": 270}}, "bottom_faces": [{"patternId": "star", "rotation": 0, "x": 3, "y": 1}, {"patternId": "J", "rotation": 90, "x": 3, "y": 2}, {"patternId": "C", "rotation": 270, "x": 2, "y": 2}, {"patternId": "6", "rotation": 0, "x": 2, "y": 3}, {"patternId": "G", "rotation": 90, "x": 2, "y": 4}, {"patternId": "star", "rotation": 90, "x": 2, "y": 5}, {"patternId": "plus", "rotation": 180, "x": 1, "y": 5}], "slot_sequence": ["FRONT", "LEFT", "TOP", "RIGHT", "BOTTOM", "BACK"], "required_slots": ["FRONT", "LEFT", "TOP", "RIGHT", "BOTTOM", "BACK"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "6", "rotation": 90}, "BOTTOM": {"patternId": "star", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 90}, "BACK": {"patternId": "plus", "rotation": 90}, "LEFT": {"patternId": "C", "rotation": 0}, "RIGHT": {"patternId": "G", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 90}, "BOTTOM": {"patternId": "star", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 90}, "BACK": {"patternId": "plus", "rotation": 90}, "LEFT": {"patternId": "C", "rotation": 0}, "RIGHT": {"patternId": "G", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C291\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> S -> S -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=J, rotation=90, flipVertical=true\n- step 2: patternId=C, rotation=270, flipVertical=true\n- step 3: patternId=6, rotation=0, flipVertical=true\n- step 4: patternId=G, rotation=90, flipVertical=true\n- step 5: patternId=star, rotation=90, flipVertical=true\n- step 6: patternId=plus, rotation=180, flipVertical=true\n- allowed patternId values for this task: J, C, 6, G, star, plus, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C291"} +{"sample_id": "C292", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> S -> W -> N -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "S", "W", "N", "N", "E"], "observed_path_faces": [{"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C292_path_sequence.png"}, "metadata": {"level_id": 292, "name": "Reconstruct 292", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-292.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["K", "I", "S", "H", "7", "smile"], "start_x": 4, "start_y": 2, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "K", "rotation": 180}, "BOTTOM": {"patternId": "smile", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 0}, "BACK": {"patternId": "H", "rotation": 270}, "LEFT": {"patternId": "7", "rotation": 270}, "RIGHT": {"patternId": "S", "rotation": 0}}, "bottom_faces": [{"patternId": "smile", "rotation": 0, "x": 4, "y": 2}, {"patternId": "7", "rotation": 180, "x": 3, "y": 2}, {"patternId": "K", "rotation": 0, "x": 2, "y": 2}, {"patternId": "I", "rotation": 180, "x": 2, "y": 3}, {"patternId": "S", "rotation": 180, "x": 1, "y": 3}, {"patternId": "K", "rotation": 90, "x": 1, "y": 2}, {"patternId": "7", "rotation": 270, "x": 1, "y": 1}, {"patternId": "I", "rotation": 0, "x": 2, "y": 1}], "slot_sequence": ["LEFT", "TOP", "FRONT", "RIGHT", "TOP", "LEFT", "FRONT"], "required_slots": ["LEFT", "TOP", "FRONT", "RIGHT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "K", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "7", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "K", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "7", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C292\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> S -> W -> N -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=7, rotation=180, flipVertical=true\n- step 2: patternId=K, rotation=0, flipVertical=true\n- step 3: patternId=I, rotation=180, flipVertical=true\n- step 4: patternId=S, rotation=180, flipVertical=true\n- step 5: patternId=K, rotation=90, flipVertical=true\n- step 6: patternId=7, rotation=270, flipVertical=true\n- step 7: patternId=I, rotation=0, flipVertical=true\n- allowed patternId values for this task: 7, K, I, S, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C292"} +{"sample_id": "C293", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> E -> E -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "E", "E", "N", "E"], "observed_path_faces": [{"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C293_path_sequence.png"}, "metadata": {"level_id": 293, "name": "Reconstruct 293", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-293.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["D", "K", "6", "D", "5", "7"], "start_x": 2, "start_y": 1, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "D", "rotation": 180}, "BOTTOM": {"patternId": "7", "rotation": 270}, "FRONT": {"patternId": "K", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 90}, "LEFT": {"patternId": "5", "rotation": 270}, "RIGHT": {"patternId": "6", "rotation": 90}}, "bottom_faces": [{"patternId": "7", "rotation": 270, "x": 2, "y": 1}, {"patternId": "5", "rotation": 180, "x": 1, "y": 1}, {"patternId": "K", "rotation": 270, "x": 1, "y": 2}, {"patternId": "7", "rotation": 180, "x": 2, "y": 2}, {"patternId": "D", "rotation": 180, "x": 3, "y": 2}, {"patternId": "5", "rotation": 0, "x": 3, "y": 1}, {"patternId": "D", "rotation": 180, "x": 4, "y": 1}], "slot_sequence": ["LEFT", "FRONT", "BOTTOM", "BACK", "LEFT", "TOP"], "required_slots": ["LEFT", "FRONT", "BOTTOM", "BACK", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "D", "rotation": 180}, "BOTTOM": {"patternId": "7", "rotation": 270}, "FRONT": {"patternId": "K", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 270}, "LEFT": {"patternId": "5", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "D", "rotation": 180}, "BOTTOM": {"patternId": "7", "rotation": 270}, "FRONT": {"patternId": "K", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 270}, "LEFT": {"patternId": "5", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C293\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> E -> E -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=5, rotation=180, flipVertical=true\n- step 2: patternId=K, rotation=270, flipVertical=true\n- step 3: patternId=7, rotation=180, flipVertical=true\n- step 4: patternId=D, rotation=180, flipVertical=true\n- step 5: patternId=5, rotation=0, flipVertical=true\n- step 6: patternId=D, rotation=180, flipVertical=true\n- allowed patternId values for this task: 5, K, 7, D, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C293"} +{"sample_id": "C294", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> E -> S -> E -> S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "E", "S", "E", "S", "N"], "observed_path_faces": [{"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C294_path_sequence.png"}, "metadata": {"level_id": 294, "name": "Reconstruct 294", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-294.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["P", "Q", "S", "4", "3", "3"], "start_x": 2, "start_y": 2, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "P", "rotation": 270}, "BOTTOM": {"patternId": "3", "rotation": 180}, "FRONT": {"patternId": "Q", "rotation": 90}, "BACK": {"patternId": "4", "rotation": 90}, "LEFT": {"patternId": "3", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 180}}, "bottom_faces": [{"patternId": "3", "rotation": 180, "x": 2, "y": 2}, {"patternId": "3", "rotation": 270, "x": 1, "y": 2}, {"patternId": "4", "rotation": 0, "x": 1, "y": 1}, {"patternId": "3", "rotation": 270, "x": 2, "y": 1}, {"patternId": "3", "rotation": 0, "x": 2, "y": 2}, {"patternId": "Q", "rotation": 90, "x": 3, "y": 2}, {"patternId": "P", "rotation": 270, "x": 3, "y": 3}, {"patternId": "Q", "rotation": 90, "x": 3, "y": 2}], "slot_sequence": ["LEFT", "BACK", "BOTTOM", "LEFT", "FRONT", "TOP", "FRONT"], "required_slots": ["LEFT", "BACK", "BOTTOM", "FRONT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "P", "rotation": 270}, "BOTTOM": {"patternId": "3", "rotation": 180}, "FRONT": {"patternId": "Q", "rotation": 90}, "BACK": {"patternId": "4", "rotation": 270}, "LEFT": {"patternId": "3", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "P", "rotation": 270}, "BOTTOM": {"patternId": "3", "rotation": 180}, "FRONT": {"patternId": "Q", "rotation": 90}, "BACK": {"patternId": "4", "rotation": 270}, "LEFT": {"patternId": "3", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C294\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> E -> S -> E -> S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=3, rotation=270, flipVertical=true\n- step 2: patternId=4, rotation=0, flipVertical=true\n- step 3: patternId=3, rotation=270, flipVertical=true\n- step 4: patternId=3, rotation=0, flipVertical=true\n- step 5: patternId=Q, rotation=90, flipVertical=true\n- step 6: patternId=P, rotation=270, flipVertical=true\n- step 7: patternId=Q, rotation=90, flipVertical=true\n- allowed patternId values for this task: 3, 4, Q, P, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C294"} +{"sample_id": "C295", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> W -> N -> W -> S -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "W", "N", "W", "S", "S", "S"], "observed_path_faces": [{"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C295_path_sequence.png"}, "metadata": {"level_id": 295, "name": "Reconstruct 295", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-295.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["2", "U", "K", "C", "O", "Q"], "start_x": 2, "start_y": 2, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "2", "rotation": 0}, "BOTTOM": {"patternId": "Q", "rotation": 270}, "FRONT": {"patternId": "U", "rotation": 180}, "BACK": {"patternId": "C", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 180}, "RIGHT": {"patternId": "K", "rotation": 0}}, "bottom_faces": [{"patternId": "Q", "rotation": 270, "x": 2, "y": 2}, {"patternId": "K", "rotation": 90, "x": 3, "y": 2}, {"patternId": "Q", "rotation": 270, "x": 2, "y": 2}, {"patternId": "C", "rotation": 180, "x": 2, "y": 1}, {"patternId": "O", "rotation": 0, "x": 1, "y": 1}, {"patternId": "Q", "rotation": 180, "x": 1, "y": 2}, {"patternId": "K", "rotation": 0, "x": 1, "y": 3}, {"patternId": "2", "rotation": 90, "x": 1, "y": 4}], "slot_sequence": ["RIGHT", "BOTTOM", "BACK", "LEFT", "BOTTOM", "RIGHT", "TOP"], "required_slots": ["RIGHT", "BOTTOM", "BACK", "LEFT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "2", "rotation": 0}, "BOTTOM": {"patternId": "Q", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "C", "rotation": 180}, "LEFT": {"patternId": "O", "rotation": 270}, "RIGHT": {"patternId": "K", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "2", "rotation": 0}, "BOTTOM": {"patternId": "Q", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "C", "rotation": 180}, "LEFT": {"patternId": "O", "rotation": 270}, "RIGHT": {"patternId": "K", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C295\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): E -> W -> N -> W -> S -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=K, rotation=90, flipVertical=true\n- step 2: patternId=Q, rotation=270, flipVertical=true\n- step 3: patternId=C, rotation=180, flipVertical=true\n- step 4: patternId=O, rotation=0, flipVertical=true\n- step 5: patternId=Q, rotation=180, flipVertical=true\n- step 6: patternId=K, rotation=0, flipVertical=true\n- step 7: patternId=2, rotation=90, flipVertical=true\n- allowed patternId values for this task: K, Q, C, O, 2, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C295"} +{"sample_id": "C296", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> S -> W -> W -> N -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "S", "W", "W", "N", "S"], "observed_path_faces": [{"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C296_path_sequence.png"}, "metadata": {"level_id": 296, "name": "Reconstruct 296", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-296.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["R", "7", "diamond", "D", "3", "M"], "start_x": 4, "start_y": 1, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "R", "rotation": 90}, "BOTTOM": {"patternId": "M", "rotation": 180}, "FRONT": {"patternId": "7", "rotation": 90}, "BACK": {"patternId": "D", "rotation": 180}, "LEFT": {"patternId": "3", "rotation": 90}, "RIGHT": {"patternId": "diamond", "rotation": 0}}, "bottom_faces": [{"patternId": "M", "rotation": 180, "x": 4, "y": 1}, {"patternId": "7", "rotation": 90, "x": 4, "y": 2}, {"patternId": "3", "rotation": 90, "x": 3, "y": 2}, {"patternId": "R", "rotation": 0, "x": 3, "y": 3}, {"patternId": "D", "rotation": 270, "x": 2, "y": 3}, {"patternId": "M", "rotation": 90, "x": 1, "y": 3}, {"patternId": "3", "rotation": 270, "x": 1, "y": 2}, {"patternId": "M", "rotation": 90, "x": 1, "y": 3}], "slot_sequence": ["FRONT", "LEFT", "TOP", "BACK", "BOTTOM", "LEFT", "BOTTOM"], "required_slots": ["FRONT", "LEFT", "TOP", "BACK", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "R", "rotation": 90}, "BOTTOM": {"patternId": "M", "rotation": 180}, "FRONT": {"patternId": "7", "rotation": 90}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "R", "rotation": 90}, "BOTTOM": {"patternId": "M", "rotation": 180}, "FRONT": {"patternId": "7", "rotation": 90}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C296\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> S -> W -> W -> N -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=7, rotation=90, flipVertical=true\n- step 2: patternId=3, rotation=90, flipVertical=true\n- step 3: patternId=R, rotation=0, flipVertical=true\n- step 4: patternId=D, rotation=270, flipVertical=true\n- step 5: patternId=M, rotation=90, flipVertical=true\n- step 6: patternId=3, rotation=270, flipVertical=true\n- step 7: patternId=M, rotation=90, flipVertical=true\n- allowed patternId values for this task: 7, 3, R, D, M, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C296"} +{"sample_id": "C297", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> W -> E -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "W", "E", "E", "E"], "observed_path_faces": [{"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C297_path_sequence.png"}, "metadata": {"level_id": 297, "name": "Reconstruct 297", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-297.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["9", "C", "M", "6", "8", "9"], "start_x": 3, "start_y": 2, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "9", "rotation": 180}, "BOTTOM": {"patternId": "9", "rotation": 90}, "FRONT": {"patternId": "C", "rotation": 270}, "BACK": {"patternId": "6", "rotation": 180}, "LEFT": {"patternId": "8", "rotation": 180}, "RIGHT": {"patternId": "M", "rotation": 0}}, "bottom_faces": [{"patternId": "9", "rotation": 90, "x": 3, "y": 2}, {"patternId": "6", "rotation": 0, "x": 3, "y": 1}, {"patternId": "8", "rotation": 0, "x": 2, "y": 1}, {"patternId": "C", "rotation": 90, "x": 1, "y": 1}, {"patternId": "8", "rotation": 0, "x": 2, "y": 1}, {"patternId": "6", "rotation": 0, "x": 3, "y": 1}, {"patternId": "M", "rotation": 180, "x": 4, "y": 1}], "slot_sequence": ["BACK", "LEFT", "FRONT", "LEFT", "BACK", "RIGHT"], "required_slots": ["BACK", "LEFT", "FRONT", "RIGHT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "C", "rotation": 270}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 270}, "RIGHT": {"patternId": "M", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "C", "rotation": 270}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 270}, "RIGHT": {"patternId": "M", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C297\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> W -> E -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=6, rotation=0, flipVertical=true\n- step 2: patternId=8, rotation=0, flipVertical=true\n- step 3: patternId=C, rotation=90, flipVertical=true\n- step 4: patternId=8, rotation=0, flipVertical=true\n- step 5: patternId=6, rotation=0, flipVertical=true\n- step 6: patternId=M, rotation=180, flipVertical=true\n- allowed patternId values for this task: 6, 8, C, M, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C297"} +{"sample_id": "C298", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> W -> W -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "W", "W", "N", "W"], "observed_path_faces": [{"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C298_path_sequence.png"}, "metadata": {"level_id": 298, "name": "Reconstruct 298", "difficulty": 3, "move_count": 6, "tier": 3, "source_level_path": "levels/reconstruct/generated-298.json", "tier_label": "Difficulty 3"}, "description": "6-move reconstruct puzzle", "net_faces": [{"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Q", "M", "T", "5", "M", "I"], "start_x": 5, "start_y": 1, "grid_width": 7, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "Q", "rotation": 0}, "BOTTOM": {"patternId": "I", "rotation": 270}, "FRONT": {"patternId": "M", "rotation": 180}, "BACK": {"patternId": "5", "rotation": 0}, "LEFT": {"patternId": "M", "rotation": 0}, "RIGHT": {"patternId": "T", "rotation": 0}}, "bottom_faces": [{"patternId": "I", "rotation": 270, "x": 5, "y": 1}, {"patternId": "M", "rotation": 180, "x": 5, "y": 2}, {"patternId": "M", "rotation": 0, "x": 4, "y": 2}, {"patternId": "5", "rotation": 0, "x": 3, "y": 2}, {"patternId": "T", "rotation": 0, "x": 2, "y": 2}, {"patternId": "I", "rotation": 180, "x": 2, "y": 1}, {"patternId": "M", "rotation": 90, "x": 1, "y": 1}], "slot_sequence": ["FRONT", "LEFT", "BACK", "RIGHT", "BOTTOM", "FRONT"], "required_slots": ["FRONT", "LEFT", "BACK", "RIGHT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "I", "rotation": 270}, "FRONT": {"patternId": "M", "rotation": 180}, "BACK": {"patternId": "5", "rotation": 180}, "LEFT": {"patternId": "M", "rotation": 90}, "RIGHT": {"patternId": "T", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "I", "rotation": 270}, "FRONT": {"patternId": "M", "rotation": 180}, "BACK": {"patternId": "5", "rotation": 180}, "LEFT": {"patternId": "M", "rotation": 90}, "RIGHT": {"patternId": "T", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C298\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 6\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> W -> W -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=M, rotation=180, flipVertical=true\n- step 2: patternId=M, rotation=0, flipVertical=true\n- step 3: patternId=5, rotation=0, flipVertical=true\n- step 4: patternId=T, rotation=0, flipVertical=true\n- step 5: patternId=I, rotation=180, flipVertical=true\n- step 6: patternId=M, rotation=90, flipVertical=true\n- allowed patternId values for this task: M, 5, T, I, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C298"} +{"sample_id": "C299", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> N -> S -> E -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "N", "S", "E", "E", "E"], "observed_path_faces": [{"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C299_path_sequence.png"}, "metadata": {"level_id": 299, "name": "Reconstruct 299", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-299.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["O", "Y", "G", "C", "G", "T"], "start_x": 1, "start_y": 1, "grid_width": 7, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "O", "rotation": 180}, "BOTTOM": {"patternId": "T", "rotation": 0}, "FRONT": {"patternId": "Y", "rotation": 90}, "BACK": {"patternId": "C", "rotation": 270}, "LEFT": {"patternId": "G", "rotation": 90}, "RIGHT": {"patternId": "G", "rotation": 270}}, "bottom_faces": [{"patternId": "T", "rotation": 0, "x": 1, "y": 1}, {"patternId": "Y", "rotation": 90, "x": 1, "y": 2}, {"patternId": "G", "rotation": 270, "x": 2, "y": 2}, {"patternId": "T", "rotation": 270, "x": 2, "y": 1}, {"patternId": "G", "rotation": 270, "x": 2, "y": 2}, {"patternId": "C", "rotation": 270, "x": 3, "y": 2}, {"patternId": "G", "rotation": 90, "x": 4, "y": 2}, {"patternId": "Y", "rotation": 90, "x": 5, "y": 2}], "slot_sequence": ["FRONT", "RIGHT", "BOTTOM", "RIGHT", "BACK", "LEFT", "FRONT"], "required_slots": ["FRONT", "RIGHT", "BOTTOM", "BACK", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "T", "rotation": 0}, "FRONT": {"patternId": "Y", "rotation": 90}, "BACK": {"patternId": "C", "rotation": 90}, "LEFT": {"patternId": "G", "rotation": 180}, "RIGHT": {"patternId": "G", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "T", "rotation": 0}, "FRONT": {"patternId": "Y", "rotation": 90}, "BACK": {"patternId": "C", "rotation": 90}, "LEFT": {"patternId": "G", "rotation": 180}, "RIGHT": {"patternId": "G", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C299\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> N -> S -> E -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Y, rotation=90, flipVertical=true\n- step 2: patternId=G, rotation=270, flipVertical=true\n- step 3: patternId=T, rotation=270, flipVertical=true\n- step 4: patternId=G, rotation=270, flipVertical=true\n- step 5: patternId=C, rotation=270, flipVertical=true\n- step 6: patternId=G, rotation=90, flipVertical=true\n- step 7: patternId=Y, rotation=90, flipVertical=true\n- allowed patternId values for this task: Y, G, T, C, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C299"} +{"sample_id": "C300", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> W -> E -> N -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "W", "E", "N", "E", "N"], "observed_path_faces": [{"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C300_path_sequence.png"}, "metadata": {"level_id": 300, "name": "Reconstruct 300", "difficulty": 3, "move_count": 7, "tier": 3, "source_level_path": "levels/reconstruct/generated-300.json", "tier_label": "Difficulty 3"}, "description": "7-move reconstruct puzzle", "net_faces": [{"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["N", "Q", "5", "R", "5", "S"], "start_x": 2, "start_y": 5, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "N", "rotation": 90}, "BOTTOM": {"patternId": "S", "rotation": 270}, "FRONT": {"patternId": "Q", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 270}, "LEFT": {"patternId": "5", "rotation": 90}, "RIGHT": {"patternId": "5", "rotation": 90}}, "bottom_faces": [{"patternId": "S", "rotation": 270, "x": 2, "y": 5}, {"patternId": "R", "rotation": 90, "x": 2, "y": 4}, {"patternId": "N", "rotation": 90, "x": 2, "y": 3}, {"patternId": "5", "rotation": 180, "x": 1, "y": 3}, {"patternId": "N", "rotation": 90, "x": 2, "y": 3}, {"patternId": "Q", "rotation": 0, "x": 2, "y": 2}, {"patternId": "5", "rotation": 90, "x": 3, "y": 2}, {"patternId": "S", "rotation": 180, "x": 3, "y": 1}], "slot_sequence": ["BACK", "TOP", "LEFT", "TOP", "FRONT", "RIGHT", "BOTTOM"], "required_slots": ["BACK", "TOP", "LEFT", "FRONT", "RIGHT", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "N", "rotation": 90}, "BOTTOM": {"patternId": "S", "rotation": 270}, "FRONT": {"patternId": "Q", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 90}, "LEFT": {"patternId": "5", "rotation": 180}, "RIGHT": {"patternId": "5", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "N", "rotation": 90}, "BOTTOM": {"patternId": "S", "rotation": 270}, "FRONT": {"patternId": "Q", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 90}, "LEFT": {"patternId": "5", "rotation": 180}, "RIGHT": {"patternId": "5", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C300\n- net_layout: standard_cross\n- difficulty: 3\n- move_count: 7\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> W -> E -> N -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=R, rotation=90, flipVertical=true\n- step 2: patternId=N, rotation=90, flipVertical=true\n- step 3: patternId=5, rotation=180, flipVertical=true\n- step 4: patternId=N, rotation=90, flipVertical=true\n- step 5: patternId=Q, rotation=0, flipVertical=true\n- step 6: patternId=5, rotation=90, flipVertical=true\n- step 7: patternId=S, rotation=180, flipVertical=true\n- allowed patternId values for this task: R, N, 5, Q, S, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C300"} +{"sample_id": "C301", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> W -> W -> W -> E -> S -> S -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "W", "W", "W", "E", "S", "S", "N", "E"], "observed_path_faces": [{"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C301_path_sequence.png"}, "metadata": {"level_id": 301, "name": "Reconstruct 301", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-301.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_down", "arrow_up", "2", "diamond", "arrow_left", "P"], "start_x": 3, "start_y": 1, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "arrow_down", "rotation": 0}, "BOTTOM": {"patternId": "P", "rotation": 180}, "FRONT": {"patternId": "arrow_up", "rotation": 270}, "BACK": {"patternId": "diamond", "rotation": 90}, "LEFT": {"patternId": "arrow_left", "rotation": 270}, "RIGHT": {"patternId": "2", "rotation": 0}}, "bottom_faces": [{"patternId": "P", "rotation": 180, "x": 3, "y": 1}, {"patternId": "2", "rotation": 90, "x": 4, "y": 1}, {"patternId": "P", "rotation": 180, "x": 3, "y": 1}, {"patternId": "arrow_left", "rotation": 180, "x": 2, "y": 1}, {"patternId": "arrow_down", "rotation": 180, "x": 1, "y": 1}, {"patternId": "arrow_left", "rotation": 180, "x": 2, "y": 1}, {"patternId": "arrow_up", "rotation": 180, "x": 2, "y": 2}, {"patternId": "2", "rotation": 270, "x": 2, "y": 3}, {"patternId": "arrow_up", "rotation": 180, "x": 2, "y": 2}, {"patternId": "P", "rotation": 90, "x": 3, "y": 2}], "slot_sequence": ["RIGHT", "BOTTOM", "LEFT", "TOP", "LEFT", "FRONT", "RIGHT", "FRONT", "BOTTOM"], "required_slots": ["RIGHT", "BOTTOM", "LEFT", "TOP", "FRONT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "arrow_down", "rotation": 0}, "BOTTOM": {"patternId": "P", "rotation": 180}, "FRONT": {"patternId": "arrow_up", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 0}, "RIGHT": {"patternId": "2", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "arrow_down", "rotation": 0}, "BOTTOM": {"patternId": "P", "rotation": 180}, "FRONT": {"patternId": "arrow_up", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 0}, "RIGHT": {"patternId": "2", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C301\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): E -> W -> W -> W -> E -> S -> S -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=2, rotation=90, flipVertical=true\n- step 2: patternId=P, rotation=180, flipVertical=true\n- step 3: patternId=arrow_left, rotation=180, flipVertical=true\n- step 4: patternId=arrow_down, rotation=180, flipVertical=true\n- step 5: patternId=arrow_left, rotation=180, flipVertical=true\n- step 6: patternId=arrow_up, rotation=180, flipVertical=true\n- step 7: patternId=2, rotation=270, flipVertical=true\n- step 8: patternId=arrow_up, rotation=180, flipVertical=true\n- step 9: patternId=P, rotation=90, flipVertical=true\n- allowed patternId values for this task: 2, P, arrow_left, arrow_down, arrow_up, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C301"} +{"sample_id": "C302", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> S -> W -> W -> N -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "S", "W", "W", "N", "W", "S"], "observed_path_faces": [{"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C302_path_sequence.png"}, "metadata": {"level_id": 302, "name": "Reconstruct 302", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-302.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["3", "V", "1", "diamond", "L", "E"], "start_x": 3, "start_y": 2, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "3", "rotation": 0}, "BOTTOM": {"patternId": "E", "rotation": 270}, "FRONT": {"patternId": "V", "rotation": 90}, "BACK": {"patternId": "diamond", "rotation": 0}, "LEFT": {"patternId": "L", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 180}}, "bottom_faces": [{"patternId": "E", "rotation": 270, "x": 3, "y": 2}, {"patternId": "diamond", "rotation": 180, "x": 3, "y": 1}, {"patternId": "1", "rotation": 0, "x": 4, "y": 1}, {"patternId": "E", "rotation": 0, "x": 4, "y": 2}, {"patternId": "diamond", "rotation": 270, "x": 3, "y": 2}, {"patternId": "3", "rotation": 90, "x": 2, "y": 2}, {"patternId": "1", "rotation": 180, "x": 2, "y": 1}, {"patternId": "V", "rotation": 90, "x": 1, "y": 1}, {"patternId": "3", "rotation": 0, "x": 1, "y": 2}], "slot_sequence": ["BACK", "RIGHT", "BOTTOM", "BACK", "TOP", "RIGHT", "FRONT", "TOP"], "required_slots": ["BACK", "RIGHT", "BOTTOM", "TOP", "FRONT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "3", "rotation": 0}, "BOTTOM": {"patternId": "E", "rotation": 270}, "FRONT": {"patternId": "V", "rotation": 90}, "BACK": {"patternId": "diamond", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "3", "rotation": 0}, "BOTTOM": {"patternId": "E", "rotation": 270}, "FRONT": {"patternId": "V", "rotation": 90}, "BACK": {"patternId": "diamond", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C302\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> S -> W -> W -> N -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=diamond, rotation=180, flipVertical=true\n- step 2: patternId=1, rotation=0, flipVertical=true\n- step 3: patternId=E, rotation=0, flipVertical=true\n- step 4: patternId=diamond, rotation=270, flipVertical=true\n- step 5: patternId=3, rotation=90, flipVertical=true\n- step 6: patternId=1, rotation=180, flipVertical=true\n- step 7: patternId=V, rotation=90, flipVertical=true\n- step 8: patternId=3, rotation=0, flipVertical=true\n- allowed patternId values for this task: diamond, 1, E, 3, V, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C302"} +{"sample_id": "C303", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> S -> S -> E -> S -> E -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "S", "S", "E", "S", "E", "N", "E"], "observed_path_faces": [{"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C303_path_sequence.png"}, "metadata": {"level_id": 303, "name": "Reconstruct 303", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-303.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["1", "I", "X", "plus", "9", "triangle"], "start_x": 2, "start_y": 1, "grid_width": 6, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "1", "rotation": 90}, "BOTTOM": {"patternId": "triangle", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 270}, "BACK": {"patternId": "plus", "rotation": 90}, "LEFT": {"patternId": "9", "rotation": 0}, "RIGHT": {"patternId": "X", "rotation": 90}}, "bottom_faces": [{"patternId": "triangle", "rotation": 0, "x": 2, "y": 1}, {"patternId": "9", "rotation": 270, "x": 1, "y": 1}, {"patternId": "I", "rotation": 180, "x": 1, "y": 2}, {"patternId": "X", "rotation": 0, "x": 1, "y": 3}, {"patternId": "plus", "rotation": 0, "x": 1, "y": 4}, {"patternId": "triangle", "rotation": 90, "x": 2, "y": 4}, {"patternId": "9", "rotation": 0, "x": 2, "y": 5}, {"patternId": "I", "rotation": 270, "x": 3, "y": 5}, {"patternId": "triangle", "rotation": 0, "x": 3, "y": 4}, {"patternId": "X", "rotation": 180, "x": 4, "y": 4}], "slot_sequence": ["LEFT", "FRONT", "RIGHT", "BACK", "BOTTOM", "LEFT", "FRONT", "BOTTOM", "RIGHT"], "required_slots": ["LEFT", "FRONT", "RIGHT", "BACK", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "triangle", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 270}, "BACK": {"patternId": "plus", "rotation": 270}, "LEFT": {"patternId": "9", "rotation": 90}, "RIGHT": {"patternId": "X", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "triangle", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 270}, "BACK": {"patternId": "plus", "rotation": 270}, "LEFT": {"patternId": "9", "rotation": 90}, "RIGHT": {"patternId": "X", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C303\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> S -> S -> E -> S -> E -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=9, rotation=270, flipVertical=true\n- step 2: patternId=I, rotation=180, flipVertical=true\n- step 3: patternId=X, rotation=0, flipVertical=true\n- step 4: patternId=plus, rotation=0, flipVertical=true\n- step 5: patternId=triangle, rotation=90, flipVertical=true\n- step 6: patternId=9, rotation=0, flipVertical=true\n- step 7: patternId=I, rotation=270, flipVertical=true\n- step 8: patternId=triangle, rotation=0, flipVertical=true\n- step 9: patternId=X, rotation=180, flipVertical=true\n- allowed patternId values for this task: 9, I, X, plus, triangle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C303"} +{"sample_id": "C304", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> N -> E -> N -> S -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "N", "E", "N", "S", "W", "W"], "observed_path_faces": [{"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C304_path_sequence.png"}, "metadata": {"level_id": 304, "name": "Reconstruct 304", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-304.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["2", "R", "5", "arrow_left", "8", "E"], "start_x": 3, "start_y": 2, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "2", "rotation": 90}, "BOTTOM": {"patternId": "E", "rotation": 0}, "FRONT": {"patternId": "R", "rotation": 270}, "BACK": {"patternId": "arrow_left", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 0}, "RIGHT": {"patternId": "5", "rotation": 0}}, "bottom_faces": [{"patternId": "E", "rotation": 0, "x": 3, "y": 2}, {"patternId": "8", "rotation": 270, "x": 2, "y": 2}, {"patternId": "R", "rotation": 180, "x": 2, "y": 3}, {"patternId": "8", "rotation": 270, "x": 2, "y": 2}, {"patternId": "E", "rotation": 0, "x": 3, "y": 2}, {"patternId": "arrow_left", "rotation": 180, "x": 3, "y": 1}, {"patternId": "E", "rotation": 0, "x": 3, "y": 2}, {"patternId": "8", "rotation": 270, "x": 2, "y": 2}, {"patternId": "2", "rotation": 270, "x": 1, "y": 2}], "slot_sequence": ["LEFT", "FRONT", "LEFT", "BOTTOM", "BACK", "BOTTOM", "LEFT", "TOP"], "required_slots": ["LEFT", "FRONT", "BOTTOM", "BACK", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "2", "rotation": 90}, "BOTTOM": {"patternId": "E", "rotation": 0}, "FRONT": {"patternId": "R", "rotation": 270}, "BACK": {"patternId": "arrow_left", "rotation": 180}, "LEFT": {"patternId": "8", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "2", "rotation": 90}, "BOTTOM": {"patternId": "E", "rotation": 0}, "FRONT": {"patternId": "R", "rotation": 270}, "BACK": {"patternId": "arrow_left", "rotation": 180}, "LEFT": {"patternId": "8", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C304\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> N -> E -> N -> S -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=8, rotation=270, flipVertical=true\n- step 2: patternId=R, rotation=180, flipVertical=true\n- step 3: patternId=8, rotation=270, flipVertical=true\n- step 4: patternId=E, rotation=0, flipVertical=true\n- step 5: patternId=arrow_left, rotation=180, flipVertical=true\n- step 6: patternId=E, rotation=0, flipVertical=true\n- step 7: patternId=8, rotation=270, flipVertical=true\n- step 8: patternId=2, rotation=270, flipVertical=true\n- allowed patternId values for this task: 8, R, E, arrow_left, 2, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C304"} +{"sample_id": "C305", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> E -> E -> S -> W -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "E", "E", "S", "W", "S", "W"], "observed_path_faces": [{"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C305_path_sequence.png"}, "metadata": {"level_id": 305, "name": "Reconstruct 305", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-305.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["8", "triangle", "Q", "I", "Y", "3"], "start_x": 1, "start_y": 2, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "8", "rotation": 90}, "BOTTOM": {"patternId": "3", "rotation": 90}, "FRONT": {"patternId": "triangle", "rotation": 180}, "BACK": {"patternId": "I", "rotation": 90}, "LEFT": {"patternId": "Y", "rotation": 270}, "RIGHT": {"patternId": "Q", "rotation": 180}}, "bottom_faces": [{"patternId": "3", "rotation": 90, "x": 1, "y": 2}, {"patternId": "Q", "rotation": 270, "x": 2, "y": 2}, {"patternId": "I", "rotation": 180, "x": 2, "y": 1}, {"patternId": "8", "rotation": 0, "x": 3, "y": 1}, {"patternId": "triangle", "rotation": 90, "x": 4, "y": 1}, {"patternId": "Q", "rotation": 90, "x": 4, "y": 2}, {"patternId": "8", "rotation": 90, "x": 3, "y": 2}, {"patternId": "I", "rotation": 270, "x": 3, "y": 3}, {"patternId": "Y", "rotation": 90, "x": 2, "y": 3}], "slot_sequence": ["RIGHT", "BACK", "TOP", "FRONT", "RIGHT", "TOP", "BACK", "LEFT"], "required_slots": ["RIGHT", "BACK", "TOP", "FRONT", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "8", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "triangle", "rotation": 180}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "Y", "rotation": 0}, "RIGHT": {"patternId": "Q", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "8", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "triangle", "rotation": 180}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "Y", "rotation": 0}, "RIGHT": {"patternId": "Q", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C305\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> E -> E -> S -> W -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Q, rotation=270, flipVertical=true\n- step 2: patternId=I, rotation=180, flipVertical=true\n- step 3: patternId=8, rotation=0, flipVertical=true\n- step 4: patternId=triangle, rotation=90, flipVertical=true\n- step 5: patternId=Q, rotation=90, flipVertical=true\n- step 6: patternId=8, rotation=90, flipVertical=true\n- step 7: patternId=I, rotation=270, flipVertical=true\n- step 8: patternId=Y, rotation=90, flipVertical=true\n- allowed patternId values for this task: Q, I, 8, triangle, Y, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C305"} +{"sample_id": "C306", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> N -> E -> N -> W -> W -> W -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "N", "E", "N", "W", "W", "W", "N", "N"], "observed_path_faces": [{"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C306_path_sequence.png"}, "metadata": {"level_id": 306, "name": "Reconstruct 306", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-306.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["smile", "heart", "I", "H", "1", "arrow_up"], "start_x": 3, "start_y": 4, "grid_width": 6, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "smile", "rotation": 90}, "BOTTOM": {"patternId": "arrow_up", "rotation": 90}, "FRONT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "H", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 270}}, "bottom_faces": [{"patternId": "arrow_up", "rotation": 90, "x": 3, "y": 4}, {"patternId": "heart", "rotation": 270, "x": 3, "y": 5}, {"patternId": "arrow_up", "rotation": 90, "x": 3, "y": 4}, {"patternId": "I", "rotation": 0, "x": 4, "y": 4}, {"patternId": "H", "rotation": 180, "x": 4, "y": 3}, {"patternId": "arrow_up", "rotation": 0, "x": 3, "y": 3}, {"patternId": "heart", "rotation": 180, "x": 2, "y": 3}, {"patternId": "smile", "rotation": 0, "x": 1, "y": 3}, {"patternId": "1", "rotation": 0, "x": 1, "y": 2}, {"patternId": "arrow_up", "rotation": 180, "x": 1, "y": 1}], "slot_sequence": ["FRONT", "BOTTOM", "RIGHT", "BACK", "BOTTOM", "FRONT", "TOP", "LEFT", "BOTTOM"], "required_slots": ["FRONT", "BOTTOM", "RIGHT", "BACK", "TOP", "LEFT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "smile", "rotation": 90}, "BOTTOM": {"patternId": "arrow_up", "rotation": 90}, "FRONT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "H", "rotation": 270}, "LEFT": {"patternId": "1", "rotation": 90}, "RIGHT": {"patternId": "I", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 90}, "BOTTOM": {"patternId": "arrow_up", "rotation": 90}, "FRONT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "H", "rotation": 270}, "LEFT": {"patternId": "1", "rotation": 90}, "RIGHT": {"patternId": "I", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C306\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> N -> E -> N -> W -> W -> W -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=heart, rotation=270, flipVertical=true\n- step 2: patternId=arrow_up, rotation=90, flipVertical=true\n- step 3: patternId=I, rotation=0, flipVertical=true\n- step 4: patternId=H, rotation=180, flipVertical=true\n- step 5: patternId=arrow_up, rotation=0, flipVertical=true\n- step 6: patternId=heart, rotation=180, flipVertical=true\n- step 7: patternId=smile, rotation=0, flipVertical=true\n- step 8: patternId=1, rotation=0, flipVertical=true\n- step 9: patternId=arrow_up, rotation=180, flipVertical=true\n- allowed patternId values for this task: heart, arrow_up, I, H, smile, 1, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C306"} +{"sample_id": "C307", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> S -> N -> W -> N -> N -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "S", "N", "W", "N", "N", "W", "S"], "observed_path_faces": [{"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C307_path_sequence.png"}, "metadata": {"level_id": 307, "name": "Reconstruct 307", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-307.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["F", "P", "5", "B", "D", "heart"], "start_x": 4, "start_y": 2, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "F", "rotation": 0}, "BOTTOM": {"patternId": "heart", "rotation": 90}, "FRONT": {"patternId": "P", "rotation": 270}, "BACK": {"patternId": "B", "rotation": 90}, "LEFT": {"patternId": "D", "rotation": 180}, "RIGHT": {"patternId": "5", "rotation": 270}}, "bottom_faces": [{"patternId": "heart", "rotation": 90, "x": 4, "y": 2}, {"patternId": "D", "rotation": 90, "x": 3, "y": 2}, {"patternId": "P", "rotation": 180, "x": 3, "y": 3}, {"patternId": "5", "rotation": 180, "x": 3, "y": 4}, {"patternId": "P", "rotation": 180, "x": 3, "y": 3}, {"patternId": "F", "rotation": 270, "x": 2, "y": 3}, {"patternId": "D", "rotation": 180, "x": 2, "y": 2}, {"patternId": "heart", "rotation": 180, "x": 2, "y": 1}, {"patternId": "B", "rotation": 0, "x": 1, "y": 1}, {"patternId": "D", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["LEFT", "FRONT", "RIGHT", "FRONT", "TOP", "LEFT", "BOTTOM", "BACK", "LEFT"], "required_slots": ["LEFT", "FRONT", "RIGHT", "TOP", "BOTTOM", "BACK"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "F", "rotation": 0}, "BOTTOM": {"patternId": "heart", "rotation": 90}, "FRONT": {"patternId": "P", "rotation": 270}, "BACK": {"patternId": "B", "rotation": 270}, "LEFT": {"patternId": "D", "rotation": 270}, "RIGHT": {"patternId": "5", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "F", "rotation": 0}, "BOTTOM": {"patternId": "heart", "rotation": 90}, "FRONT": {"patternId": "P", "rotation": 270}, "BACK": {"patternId": "B", "rotation": 270}, "LEFT": {"patternId": "D", "rotation": 270}, "RIGHT": {"patternId": "5", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C307\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> S -> N -> W -> N -> N -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=D, rotation=90, flipVertical=true\n- step 2: patternId=P, rotation=180, flipVertical=true\n- step 3: patternId=5, rotation=180, flipVertical=true\n- step 4: patternId=P, rotation=180, flipVertical=true\n- step 5: patternId=F, rotation=270, flipVertical=true\n- step 6: patternId=D, rotation=180, flipVertical=true\n- step 7: patternId=heart, rotation=180, flipVertical=true\n- step 8: patternId=B, rotation=0, flipVertical=true\n- step 9: patternId=D, rotation=90, flipVertical=true\n- allowed patternId values for this task: D, P, 5, F, heart, B, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C307"} +{"sample_id": "C308", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> N -> W -> W -> S -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "N", "W", "W", "S", "E", "E"], "observed_path_faces": [{"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C308_path_sequence.png"}, "metadata": {"level_id": 308, "name": "Reconstruct 308", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-308.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["K", "1", "arrow_up", "U", "K", "Q"], "start_x": 1, "start_y": 2, "grid_width": 5, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "K", "rotation": 0}, "BOTTOM": {"patternId": "Q", "rotation": 270}, "FRONT": {"patternId": "1", "rotation": 0}, "BACK": {"patternId": "U", "rotation": 90}, "LEFT": {"patternId": "K", "rotation": 270}, "RIGHT": {"patternId": "arrow_up", "rotation": 270}}, "bottom_faces": [{"patternId": "Q", "rotation": 270, "x": 1, "y": 2}, {"patternId": "arrow_up", "rotation": 0, "x": 2, "y": 2}, {"patternId": "K", "rotation": 180, "x": 3, "y": 2}, {"patternId": "U", "rotation": 90, "x": 3, "y": 1}, {"patternId": "arrow_up", "rotation": 270, "x": 2, "y": 1}, {"patternId": "1", "rotation": 0, "x": 1, "y": 1}, {"patternId": "K", "rotation": 0, "x": 1, "y": 2}, {"patternId": "arrow_up", "rotation": 180, "x": 2, "y": 2}, {"patternId": "Q", "rotation": 90, "x": 3, "y": 2}], "slot_sequence": ["RIGHT", "TOP", "BACK", "RIGHT", "FRONT", "TOP", "RIGHT", "BOTTOM"], "required_slots": ["RIGHT", "TOP", "BACK", "FRONT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "K", "rotation": 0}, "BOTTOM": {"patternId": "Q", "rotation": 270}, "FRONT": {"patternId": "1", "rotation": 0}, "BACK": {"patternId": "U", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_up", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "K", "rotation": 0}, "BOTTOM": {"patternId": "Q", "rotation": 270}, "FRONT": {"patternId": "1", "rotation": 0}, "BACK": {"patternId": "U", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_up", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C308\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> N -> W -> W -> S -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_up, rotation=0, flipVertical=true\n- step 2: patternId=K, rotation=180, flipVertical=true\n- step 3: patternId=U, rotation=90, flipVertical=true\n- step 4: patternId=arrow_up, rotation=270, flipVertical=true\n- step 5: patternId=1, rotation=0, flipVertical=true\n- step 6: patternId=K, rotation=0, flipVertical=true\n- step 7: patternId=arrow_up, rotation=180, flipVertical=true\n- step 8: patternId=Q, rotation=90, flipVertical=true\n- allowed patternId values for this task: arrow_up, K, U, 1, Q, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C308"} +{"sample_id": "C309", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> E -> N -> W -> E -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "E", "N", "W", "E", "N", "E"], "observed_path_faces": [{"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C309_path_sequence.png"}, "metadata": {"level_id": 309, "name": "Reconstruct 309", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-309.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["square", "Y", "6", "P", "3", "arrow_left"], "start_x": 2, "start_y": 4, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "square", "rotation": 90}, "BOTTOM": {"patternId": "arrow_left", "rotation": 90}, "FRONT": {"patternId": "Y", "rotation": 180}, "BACK": {"patternId": "P", "rotation": 270}, "LEFT": {"patternId": "3", "rotation": 270}, "RIGHT": {"patternId": "6", "rotation": 90}}, "bottom_faces": [{"patternId": "arrow_left", "rotation": 90, "x": 2, "y": 4}, {"patternId": "3", "rotation": 180, "x": 1, "y": 4}, {"patternId": "P", "rotation": 180, "x": 1, "y": 3}, {"patternId": "arrow_left", "rotation": 180, "x": 2, "y": 3}, {"patternId": "6", "rotation": 270, "x": 2, "y": 2}, {"patternId": "P", "rotation": 90, "x": 1, "y": 2}, {"patternId": "6", "rotation": 270, "x": 2, "y": 2}, {"patternId": "square", "rotation": 0, "x": 2, "y": 1}, {"patternId": "Y", "rotation": 90, "x": 3, "y": 1}], "slot_sequence": ["LEFT", "BACK", "BOTTOM", "RIGHT", "BACK", "RIGHT", "TOP", "FRONT"], "required_slots": ["LEFT", "BACK", "BOTTOM", "RIGHT", "TOP", "FRONT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "square", "rotation": 90}, "BOTTOM": {"patternId": "arrow_left", "rotation": 90}, "FRONT": {"patternId": "Y", "rotation": 180}, "BACK": {"patternId": "P", "rotation": 90}, "LEFT": {"patternId": "3", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "square", "rotation": 90}, "BOTTOM": {"patternId": "arrow_left", "rotation": 90}, "FRONT": {"patternId": "Y", "rotation": 180}, "BACK": {"patternId": "P", "rotation": 90}, "LEFT": {"patternId": "3", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C309\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> E -> N -> W -> E -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=3, rotation=180, flipVertical=true\n- step 2: patternId=P, rotation=180, flipVertical=true\n- step 3: patternId=arrow_left, rotation=180, flipVertical=true\n- step 4: patternId=6, rotation=270, flipVertical=true\n- step 5: patternId=P, rotation=90, flipVertical=true\n- step 6: patternId=6, rotation=270, flipVertical=true\n- step 7: patternId=square, rotation=0, flipVertical=true\n- step 8: patternId=Y, rotation=90, flipVertical=true\n- allowed patternId values for this task: 3, P, arrow_left, 6, square, Y, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C309"} +{"sample_id": "C310", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> W -> S -> E -> S -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "W", "S", "E", "S", "E", "N"], "observed_path_faces": [{"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C310_path_sequence.png"}, "metadata": {"level_id": 310, "name": "Reconstruct 310", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-310.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["K", "W", "triangle", "G", "M", "F"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "K", "rotation": 180}, "BOTTOM": {"patternId": "F", "rotation": 180}, "FRONT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "G", "rotation": 90}, "LEFT": {"patternId": "M", "rotation": 180}, "RIGHT": {"patternId": "triangle", "rotation": 270}}, "bottom_faces": [{"patternId": "F", "rotation": 180, "x": 3, "y": 1}, {"patternId": "M", "rotation": 90, "x": 2, "y": 1}, {"patternId": "W", "rotation": 0, "x": 2, "y": 2}, {"patternId": "K", "rotation": 90, "x": 1, "y": 2}, {"patternId": "triangle", "rotation": 90, "x": 1, "y": 3}, {"patternId": "W", "rotation": 270, "x": 2, "y": 3}, {"patternId": "F", "rotation": 0, "x": 2, "y": 4}, {"patternId": "M", "rotation": 270, "x": 3, "y": 4}, {"patternId": "W", "rotation": 180, "x": 3, "y": 3}], "slot_sequence": ["LEFT", "FRONT", "TOP", "RIGHT", "FRONT", "BOTTOM", "LEFT", "FRONT"], "required_slots": ["LEFT", "FRONT", "TOP", "RIGHT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "K", "rotation": 180}, "BOTTOM": {"patternId": "F", "rotation": 180}, "FRONT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "M", "rotation": 270}, "RIGHT": {"patternId": "triangle", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "K", "rotation": 180}, "BOTTOM": {"patternId": "F", "rotation": 180}, "FRONT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "M", "rotation": 270}, "RIGHT": {"patternId": "triangle", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C310\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> W -> S -> E -> S -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=M, rotation=90, flipVertical=true\n- step 2: patternId=W, rotation=0, flipVertical=true\n- step 3: patternId=K, rotation=90, flipVertical=true\n- step 4: patternId=triangle, rotation=90, flipVertical=true\n- step 5: patternId=W, rotation=270, flipVertical=true\n- step 6: patternId=F, rotation=0, flipVertical=true\n- step 7: patternId=M, rotation=270, flipVertical=true\n- step 8: patternId=W, rotation=180, flipVertical=true\n- allowed patternId values for this task: M, W, K, triangle, F, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C310"} +{"sample_id": "C311", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> N -> E -> E -> W -> N -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "N", "E", "E", "W", "N", "W", "N"], "observed_path_faces": [{"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C311_path_sequence.png"}, "metadata": {"level_id": 311, "name": "Reconstruct 311", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-311.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["C", "P", "R", "7", "F", "square"], "start_x": 1, "start_y": 5, "grid_width": 6, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "C", "rotation": 0}, "BOTTOM": {"patternId": "square", "rotation": 270}, "FRONT": {"patternId": "P", "rotation": 270}, "BACK": {"patternId": "7", "rotation": 270}, "LEFT": {"patternId": "F", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 270}}, "bottom_faces": [{"patternId": "square", "rotation": 270, "x": 1, "y": 5}, {"patternId": "R", "rotation": 0, "x": 2, "y": 5}, {"patternId": "7", "rotation": 0, "x": 2, "y": 4}, {"patternId": "F", "rotation": 90, "x": 2, "y": 3}, {"patternId": "C", "rotation": 0, "x": 3, "y": 3}, {"patternId": "R", "rotation": 180, "x": 4, "y": 3}, {"patternId": "C", "rotation": 0, "x": 3, "y": 3}, {"patternId": "P", "rotation": 270, "x": 3, "y": 2}, {"patternId": "F", "rotation": 0, "x": 2, "y": 2}, {"patternId": "square", "rotation": 0, "x": 2, "y": 1}], "slot_sequence": ["RIGHT", "BACK", "LEFT", "TOP", "RIGHT", "TOP", "FRONT", "LEFT", "BOTTOM"], "required_slots": ["RIGHT", "BACK", "LEFT", "TOP", "FRONT", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "C", "rotation": 0}, "BOTTOM": {"patternId": "square", "rotation": 270}, "FRONT": {"patternId": "P", "rotation": 270}, "BACK": {"patternId": "7", "rotation": 90}, "LEFT": {"patternId": "F", "rotation": 90}, "RIGHT": {"patternId": "R", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "C", "rotation": 0}, "BOTTOM": {"patternId": "square", "rotation": 270}, "FRONT": {"patternId": "P", "rotation": 270}, "BACK": {"patternId": "7", "rotation": 90}, "LEFT": {"patternId": "F", "rotation": 90}, "RIGHT": {"patternId": "R", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C311\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> N -> E -> E -> W -> N -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=R, rotation=0, flipVertical=true\n- step 2: patternId=7, rotation=0, flipVertical=true\n- step 3: patternId=F, rotation=90, flipVertical=true\n- step 4: patternId=C, rotation=0, flipVertical=true\n- step 5: patternId=R, rotation=180, flipVertical=true\n- step 6: patternId=C, rotation=0, flipVertical=true\n- step 7: patternId=P, rotation=270, flipVertical=true\n- step 8: patternId=F, rotation=0, flipVertical=true\n- step 9: patternId=square, rotation=0, flipVertical=true\n- allowed patternId values for this task: R, 7, F, C, P, square, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C311"} +{"sample_id": "C312", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> W -> N -> N -> S -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "W", "N", "N", "S", "W", "N"], "observed_path_faces": [{"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C312_path_sequence.png"}, "metadata": {"level_id": 312, "name": "Reconstruct 312", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-312.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["T", "4", "plus", "arrow_left", "O", "F"], "start_x": 4, "start_y": 2, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "T", "rotation": 270}, "BOTTOM": {"patternId": "F", "rotation": 180}, "FRONT": {"patternId": "4", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 270}, "RIGHT": {"patternId": "plus", "rotation": 180}}, "bottom_faces": [{"patternId": "F", "rotation": 180, "x": 4, "y": 2}, {"patternId": "O", "rotation": 180, "x": 3, "y": 2}, {"patternId": "4", "rotation": 270, "x": 3, "y": 3}, {"patternId": "T", "rotation": 180, "x": 2, "y": 3}, {"patternId": "O", "rotation": 270, "x": 2, "y": 2}, {"patternId": "F", "rotation": 270, "x": 2, "y": 1}, {"patternId": "O", "rotation": 270, "x": 2, "y": 2}, {"patternId": "arrow_left", "rotation": 0, "x": 1, "y": 2}, {"patternId": "F", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "FRONT", "TOP", "LEFT", "BOTTOM", "LEFT", "BACK", "BOTTOM"], "required_slots": ["LEFT", "FRONT", "TOP", "BOTTOM", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "T", "rotation": 270}, "BOTTOM": {"patternId": "F", "rotation": 180}, "FRONT": {"patternId": "4", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 180}, "LEFT": {"patternId": "O", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "T", "rotation": 270}, "BOTTOM": {"patternId": "F", "rotation": 180}, "FRONT": {"patternId": "4", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 180}, "LEFT": {"patternId": "O", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C312\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> W -> N -> N -> S -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=O, rotation=180, flipVertical=true\n- step 2: patternId=4, rotation=270, flipVertical=true\n- step 3: patternId=T, rotation=180, flipVertical=true\n- step 4: patternId=O, rotation=270, flipVertical=true\n- step 5: patternId=F, rotation=270, flipVertical=true\n- step 6: patternId=O, rotation=270, flipVertical=true\n- step 7: patternId=arrow_left, rotation=0, flipVertical=true\n- step 8: patternId=F, rotation=0, flipVertical=true\n- allowed patternId values for this task: O, 4, T, F, arrow_left, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C312"} +{"sample_id": "C313", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> N -> E -> S -> S -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "N", "E", "S", "S", "E", "E"], "observed_path_faces": [{"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C313_path_sequence.png"}, "metadata": {"level_id": 313, "name": "Reconstruct 313", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-313.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["plus", "G", "N", "B", "W", "O"], "start_x": 2, "start_y": 3, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "plus", "rotation": 90}, "BOTTOM": {"patternId": "O", "rotation": 180}, "FRONT": {"patternId": "G", "rotation": 180}, "BACK": {"patternId": "B", "rotation": 90}, "LEFT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "N", "rotation": 90}}, "bottom_faces": [{"patternId": "O", "rotation": 180, "x": 2, "y": 3}, {"patternId": "W", "rotation": 0, "x": 1, "y": 3}, {"patternId": "B", "rotation": 0, "x": 1, "y": 2}, {"patternId": "N", "rotation": 0, "x": 1, "y": 1}, {"patternId": "O", "rotation": 0, "x": 2, "y": 1}, {"patternId": "B", "rotation": 90, "x": 2, "y": 2}, {"patternId": "plus", "rotation": 270, "x": 2, "y": 3}, {"patternId": "W", "rotation": 0, "x": 3, "y": 3}, {"patternId": "O", "rotation": 180, "x": 4, "y": 3}], "slot_sequence": ["LEFT", "BACK", "RIGHT", "BOTTOM", "BACK", "TOP", "LEFT", "BOTTOM"], "required_slots": ["LEFT", "BACK", "RIGHT", "BOTTOM", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "plus", "rotation": 90}, "BOTTOM": {"patternId": "O", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 270}, "LEFT": {"patternId": "W", "rotation": 180}, "RIGHT": {"patternId": "N", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "plus", "rotation": 90}, "BOTTOM": {"patternId": "O", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 270}, "LEFT": {"patternId": "W", "rotation": 180}, "RIGHT": {"patternId": "N", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C313\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> N -> E -> S -> S -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=W, rotation=0, flipVertical=true\n- step 2: patternId=B, rotation=0, flipVertical=true\n- step 3: patternId=N, rotation=0, flipVertical=true\n- step 4: patternId=O, rotation=0, flipVertical=true\n- step 5: patternId=B, rotation=90, flipVertical=true\n- step 6: patternId=plus, rotation=270, flipVertical=true\n- step 7: patternId=W, rotation=0, flipVertical=true\n- step 8: patternId=O, rotation=180, flipVertical=true\n- allowed patternId values for this task: W, B, N, O, plus, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C313"} +{"sample_id": "C314", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> N -> E -> N -> N -> W -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "N", "E", "N", "N", "W", "N", "N"], "observed_path_faces": [{"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C314_path_sequence.png"}, "metadata": {"level_id": 314, "name": "Reconstruct 314", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-314.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["G", "square", "B", "K", "J", "1"], "start_x": 1, "start_y": 5, "grid_width": 4, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "G", "rotation": 270}, "BOTTOM": {"patternId": "1", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 270}, "BACK": {"patternId": "K", "rotation": 0}, "LEFT": {"patternId": "J", "rotation": 270}, "RIGHT": {"patternId": "B", "rotation": 270}}, "bottom_faces": [{"patternId": "1", "rotation": 0, "x": 1, "y": 5}, {"patternId": "square", "rotation": 270, "x": 1, "y": 6}, {"patternId": "1", "rotation": 0, "x": 1, "y": 5}, {"patternId": "B", "rotation": 0, "x": 2, "y": 5}, {"patternId": "K", "rotation": 90, "x": 2, "y": 4}, {"patternId": "J", "rotation": 0, "x": 2, "y": 3}, {"patternId": "1", "rotation": 180, "x": 1, "y": 3}, {"patternId": "square", "rotation": 90, "x": 1, "y": 2}, {"patternId": "G", "rotation": 90, "x": 1, "y": 1}], "slot_sequence": ["FRONT", "BOTTOM", "RIGHT", "BACK", "LEFT", "BOTTOM", "FRONT", "TOP"], "required_slots": ["FRONT", "BOTTOM", "RIGHT", "BACK", "LEFT", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "G", "rotation": 270}, "BOTTOM": {"patternId": "1", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 270}, "BACK": {"patternId": "K", "rotation": 180}, "LEFT": {"patternId": "J", "rotation": 0}, "RIGHT": {"patternId": "B", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "G", "rotation": 270}, "BOTTOM": {"patternId": "1", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 270}, "BACK": {"patternId": "K", "rotation": 180}, "LEFT": {"patternId": "J", "rotation": 0}, "RIGHT": {"patternId": "B", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C314\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> N -> E -> N -> N -> W -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=square, rotation=270, flipVertical=true\n- step 2: patternId=1, rotation=0, flipVertical=true\n- step 3: patternId=B, rotation=0, flipVertical=true\n- step 4: patternId=K, rotation=90, flipVertical=true\n- step 5: patternId=J, rotation=0, flipVertical=true\n- step 6: patternId=1, rotation=180, flipVertical=true\n- step 7: patternId=square, rotation=90, flipVertical=true\n- step 8: patternId=G, rotation=90, flipVertical=true\n- allowed patternId values for this task: square, 1, B, K, J, G, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C314"} +{"sample_id": "C315", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> S -> S -> N -> E -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "S", "S", "N", "E", "S", "E"], "observed_path_faces": [{"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C315_path_sequence.png"}, "metadata": {"level_id": 315, "name": "Reconstruct 315", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-315.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Q", "M", "heart", "triangle", "O", "5"], "start_x": 1, "start_y": 2, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "Q", "rotation": 90}, "BOTTOM": {"patternId": "5", "rotation": 0}, "FRONT": {"patternId": "M", "rotation": 180}, "BACK": {"patternId": "triangle", "rotation": 90}, "LEFT": {"patternId": "O", "rotation": 180}, "RIGHT": {"patternId": "heart", "rotation": 180}}, "bottom_faces": [{"patternId": "5", "rotation": 0, "x": 1, "y": 2}, {"patternId": "triangle", "rotation": 270, "x": 1, "y": 1}, {"patternId": "heart", "rotation": 0, "x": 2, "y": 1}, {"patternId": "5", "rotation": 90, "x": 2, "y": 2}, {"patternId": "O", "rotation": 180, "x": 2, "y": 3}, {"patternId": "5", "rotation": 90, "x": 2, "y": 2}, {"patternId": "M", "rotation": 270, "x": 3, "y": 2}, {"patternId": "O", "rotation": 270, "x": 3, "y": 3}, {"patternId": "Q", "rotation": 90, "x": 4, "y": 3}], "slot_sequence": ["BACK", "RIGHT", "BOTTOM", "LEFT", "BOTTOM", "FRONT", "LEFT", "TOP"], "required_slots": ["BACK", "RIGHT", "BOTTOM", "LEFT", "FRONT", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "Q", "rotation": 90}, "BOTTOM": {"patternId": "5", "rotation": 0}, "FRONT": {"patternId": "M", "rotation": 180}, "BACK": {"patternId": "triangle", "rotation": 270}, "LEFT": {"patternId": "O", "rotation": 270}, "RIGHT": {"patternId": "heart", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "Q", "rotation": 90}, "BOTTOM": {"patternId": "5", "rotation": 0}, "FRONT": {"patternId": "M", "rotation": 180}, "BACK": {"patternId": "triangle", "rotation": 270}, "LEFT": {"patternId": "O", "rotation": 270}, "RIGHT": {"patternId": "heart", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C315\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> S -> S -> N -> E -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=triangle, rotation=270, flipVertical=true\n- step 2: patternId=heart, rotation=0, flipVertical=true\n- step 3: patternId=5, rotation=90, flipVertical=true\n- step 4: patternId=O, rotation=180, flipVertical=true\n- step 5: patternId=5, rotation=90, flipVertical=true\n- step 6: patternId=M, rotation=270, flipVertical=true\n- step 7: patternId=O, rotation=270, flipVertical=true\n- step 8: patternId=Q, rotation=90, flipVertical=true\n- allowed patternId values for this task: triangle, heart, 5, O, M, Q, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C315"} +{"sample_id": "C316", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> N -> E -> N -> E -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "N", "E", "N", "E", "E", "N"], "observed_path_faces": [{"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C316_path_sequence.png"}, "metadata": {"level_id": 316, "name": "Reconstruct 316", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-316.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["A", "7", "Q", "1", "arrow_down", "B"], "start_x": 1, "start_y": 6, "grid_width": 6, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "A", "rotation": 270}, "BOTTOM": {"patternId": "B", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 270}, "BACK": {"patternId": "1", "rotation": 0}, "LEFT": {"patternId": "arrow_down", "rotation": 0}, "RIGHT": {"patternId": "Q", "rotation": 90}}, "bottom_faces": [{"patternId": "B", "rotation": 0, "x": 1, "y": 6}, {"patternId": "1", "rotation": 180, "x": 1, "y": 5}, {"patternId": "A", "rotation": 270, "x": 1, "y": 4}, {"patternId": "7", "rotation": 270, "x": 1, "y": 3}, {"patternId": "Q", "rotation": 90, "x": 2, "y": 3}, {"patternId": "B", "rotation": 270, "x": 2, "y": 2}, {"patternId": "1", "rotation": 90, "x": 3, "y": 2}, {"patternId": "A", "rotation": 180, "x": 4, "y": 2}, {"patternId": "arrow_down", "rotation": 0, "x": 4, "y": 1}], "slot_sequence": ["BACK", "TOP", "FRONT", "RIGHT", "BOTTOM", "BACK", "TOP", "LEFT"], "required_slots": ["BACK", "TOP", "FRONT", "RIGHT", "BOTTOM", "LEFT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "A", "rotation": 270}, "BOTTOM": {"patternId": "B", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 270}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "arrow_down", "rotation": 90}, "RIGHT": {"patternId": "Q", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "A", "rotation": 270}, "BOTTOM": {"patternId": "B", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 270}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "arrow_down", "rotation": 90}, "RIGHT": {"patternId": "Q", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C316\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> N -> E -> N -> E -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=1, rotation=180, flipVertical=true\n- step 2: patternId=A, rotation=270, flipVertical=true\n- step 3: patternId=7, rotation=270, flipVertical=true\n- step 4: patternId=Q, rotation=90, flipVertical=true\n- step 5: patternId=B, rotation=270, flipVertical=true\n- step 6: patternId=1, rotation=90, flipVertical=true\n- step 7: patternId=A, rotation=180, flipVertical=true\n- step 8: patternId=arrow_down, rotation=0, flipVertical=true\n- allowed patternId values for this task: 1, A, 7, Q, B, arrow_down, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C316"} +{"sample_id": "C317", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> E -> N -> W -> E -> S -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "E", "N", "W", "E", "S", "S", "W"], "observed_path_faces": [{"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C317_path_sequence.png"}, "metadata": {"level_id": 317, "name": "Reconstruct 317", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-317.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["6", "9", "D", "heart", "F", "diamond"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "6", "rotation": 180}, "BOTTOM": {"patternId": "diamond", "rotation": 90}, "FRONT": {"patternId": "9", "rotation": 180}, "BACK": {"patternId": "heart", "rotation": 270}, "LEFT": {"patternId": "F", "rotation": 90}, "RIGHT": {"patternId": "D", "rotation": 270}}, "bottom_faces": [{"patternId": "diamond", "rotation": 90, "x": 2, "y": 1}, {"patternId": "9", "rotation": 180, "x": 2, "y": 2}, {"patternId": "F", "rotation": 90, "x": 1, "y": 2}, {"patternId": "9", "rotation": 180, "x": 2, "y": 2}, {"patternId": "diamond", "rotation": 90, "x": 2, "y": 1}, {"patternId": "F", "rotation": 0, "x": 1, "y": 1}, {"patternId": "diamond", "rotation": 90, "x": 2, "y": 1}, {"patternId": "9", "rotation": 180, "x": 2, "y": 2}, {"patternId": "6", "rotation": 180, "x": 2, "y": 3}, {"patternId": "F", "rotation": 180, "x": 1, "y": 3}], "slot_sequence": ["FRONT", "LEFT", "FRONT", "BOTTOM", "LEFT", "BOTTOM", "FRONT", "TOP", "LEFT"], "required_slots": ["FRONT", "LEFT", "BOTTOM", "TOP"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "6", "rotation": 180}, "BOTTOM": {"patternId": "diamond", "rotation": 90}, "FRONT": {"patternId": "9", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "F", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 180}, "BOTTOM": {"patternId": "diamond", "rotation": 90}, "FRONT": {"patternId": "9", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "F", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C317\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> E -> N -> W -> E -> S -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=9, rotation=180, flipVertical=true\n- step 2: patternId=F, rotation=90, flipVertical=true\n- step 3: patternId=9, rotation=180, flipVertical=true\n- step 4: patternId=diamond, rotation=90, flipVertical=true\n- step 5: patternId=F, rotation=0, flipVertical=true\n- step 6: patternId=diamond, rotation=90, flipVertical=true\n- step 7: patternId=9, rotation=180, flipVertical=true\n- step 8: patternId=6, rotation=180, flipVertical=true\n- step 9: patternId=F, rotation=180, flipVertical=true\n- allowed patternId values for this task: 9, F, diamond, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C317"} +{"sample_id": "C318", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> N -> E -> S -> S -> W -> W -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "N", "E", "S", "S", "W", "W", "N", "N"], "observed_path_faces": [{"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C318_path_sequence.png"}, "metadata": {"level_id": 318, "name": "Reconstruct 318", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-318.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["L", "9", "I", "heart", "F", "arrow_down"], "start_x": 2, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "L", "rotation": 180}, "BOTTOM": {"patternId": "arrow_down", "rotation": 0}, "FRONT": {"patternId": "9", "rotation": 180}, "BACK": {"patternId": "heart", "rotation": 270}, "LEFT": {"patternId": "F", "rotation": 270}, "RIGHT": {"patternId": "I", "rotation": 180}}, "bottom_faces": [{"patternId": "arrow_down", "rotation": 0, "x": 2, "y": 1}, {"patternId": "9", "rotation": 180, "x": 2, "y": 2}, {"patternId": "arrow_down", "rotation": 0, "x": 2, "y": 1}, {"patternId": "I", "rotation": 270, "x": 3, "y": 1}, {"patternId": "9", "rotation": 270, "x": 3, "y": 2}, {"patternId": "F", "rotation": 0, "x": 3, "y": 3}, {"patternId": "arrow_down", "rotation": 180, "x": 2, "y": 3}, {"patternId": "I", "rotation": 90, "x": 1, "y": 3}, {"patternId": "9", "rotation": 90, "x": 1, "y": 2}, {"patternId": "F", "rotation": 180, "x": 1, "y": 1}], "slot_sequence": ["FRONT", "BOTTOM", "RIGHT", "FRONT", "LEFT", "BOTTOM", "RIGHT", "FRONT", "LEFT"], "required_slots": ["FRONT", "BOTTOM", "RIGHT", "LEFT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_down", "rotation": 0}, "FRONT": {"patternId": "9", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "F", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_down", "rotation": 0}, "FRONT": {"patternId": "9", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "F", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C318\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> N -> E -> S -> S -> W -> W -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=9, rotation=180, flipVertical=true\n- step 2: patternId=arrow_down, rotation=0, flipVertical=true\n- step 3: patternId=I, rotation=270, flipVertical=true\n- step 4: patternId=9, rotation=270, flipVertical=true\n- step 5: patternId=F, rotation=0, flipVertical=true\n- step 6: patternId=arrow_down, rotation=180, flipVertical=true\n- step 7: patternId=I, rotation=90, flipVertical=true\n- step 8: patternId=9, rotation=90, flipVertical=true\n- step 9: patternId=F, rotation=180, flipVertical=true\n- allowed patternId values for this task: 9, arrow_down, I, F, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C318"} +{"sample_id": "C319", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> N -> W -> N -> N -> N -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "N", "W", "N", "N", "N", "W", "S"], "observed_path_faces": [{"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C319_path_sequence.png"}, "metadata": {"level_id": 319, "name": "Reconstruct 319", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-319.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["X", "C", "1", "heart", "O", "8"], "start_x": 5, "start_y": 5, "grid_width": 7, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "X", "rotation": 270}, "BOTTOM": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "C", "rotation": 180}, "BACK": {"patternId": "heart", "rotation": 180}, "LEFT": {"patternId": "O", "rotation": 270}, "RIGHT": {"patternId": "1", "rotation": 180}}, "bottom_faces": [{"patternId": "8", "rotation": 180, "x": 5, "y": 5}, {"patternId": "O", "rotation": 180, "x": 4, "y": 5}, {"patternId": "X", "rotation": 90, "x": 3, "y": 5}, {"patternId": "heart", "rotation": 180, "x": 3, "y": 4}, {"patternId": "1", "rotation": 180, "x": 2, "y": 4}, {"patternId": "8", "rotation": 90, "x": 2, "y": 3}, {"patternId": "O", "rotation": 90, "x": 2, "y": 2}, {"patternId": "X", "rotation": 0, "x": 2, "y": 1}, {"patternId": "C", "rotation": 270, "x": 1, "y": 1}, {"patternId": "O", "rotation": 0, "x": 1, "y": 2}], "slot_sequence": ["LEFT", "TOP", "BACK", "RIGHT", "BOTTOM", "LEFT", "TOP", "FRONT", "LEFT"], "required_slots": ["LEFT", "TOP", "BACK", "RIGHT", "BOTTOM", "FRONT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "X", "rotation": 270}, "BOTTOM": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "C", "rotation": 180}, "BACK": {"patternId": "heart", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "X", "rotation": 270}, "BOTTOM": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "C", "rotation": 180}, "BACK": {"patternId": "heart", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C319\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> N -> W -> N -> N -> N -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=O, rotation=180, flipVertical=true\n- step 2: patternId=X, rotation=90, flipVertical=true\n- step 3: patternId=heart, rotation=180, flipVertical=true\n- step 4: patternId=1, rotation=180, flipVertical=true\n- step 5: patternId=8, rotation=90, flipVertical=true\n- step 6: patternId=O, rotation=90, flipVertical=true\n- step 7: patternId=X, rotation=0, flipVertical=true\n- step 8: patternId=C, rotation=270, flipVertical=true\n- step 9: patternId=O, rotation=0, flipVertical=true\n- allowed patternId values for this task: O, X, heart, 1, 8, C, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C319"} +{"sample_id": "C320", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> S -> S -> W -> N -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "S", "S", "W", "N", "N", "W"], "observed_path_faces": [{"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C320_path_sequence.png"}, "metadata": {"level_id": 320, "name": "Reconstruct 320", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-320.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["S", "U", "2", "3", "6", "W"], "start_x": 4, "start_y": 2, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "S", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 180}, "FRONT": {"patternId": "U", "rotation": 270}, "BACK": {"patternId": "3", "rotation": 90}, "LEFT": {"patternId": "6", "rotation": 90}, "RIGHT": {"patternId": "2", "rotation": 270}}, "bottom_faces": [{"patternId": "W", "rotation": 180, "x": 4, "y": 2}, {"patternId": "6", "rotation": 0, "x": 3, "y": 2}, {"patternId": "3", "rotation": 0, "x": 3, "y": 1}, {"patternId": "6", "rotation": 0, "x": 3, "y": 2}, {"patternId": "U", "rotation": 180, "x": 3, "y": 3}, {"patternId": "S", "rotation": 270, "x": 2, "y": 3}, {"patternId": "6", "rotation": 90, "x": 2, "y": 2}, {"patternId": "W", "rotation": 270, "x": 2, "y": 1}, {"patternId": "3", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "BACK", "LEFT", "FRONT", "TOP", "LEFT", "BOTTOM", "BACK"], "required_slots": ["LEFT", "BACK", "FRONT", "TOP", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "S", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 180}, "FRONT": {"patternId": "U", "rotation": 270}, "BACK": {"patternId": "3", "rotation": 270}, "LEFT": {"patternId": "6", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 180}, "FRONT": {"patternId": "U", "rotation": 270}, "BACK": {"patternId": "3", "rotation": 270}, "LEFT": {"patternId": "6", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C320\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> S -> S -> W -> N -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=6, rotation=0, flipVertical=true\n- step 2: patternId=3, rotation=0, flipVertical=true\n- step 3: patternId=6, rotation=0, flipVertical=true\n- step 4: patternId=U, rotation=180, flipVertical=true\n- step 5: patternId=S, rotation=270, flipVertical=true\n- step 6: patternId=6, rotation=90, flipVertical=true\n- step 7: patternId=W, rotation=270, flipVertical=true\n- step 8: patternId=3, rotation=0, flipVertical=true\n- allowed patternId values for this task: 6, 3, U, S, W, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C320"} +{"sample_id": "C321", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> E -> E -> N -> S -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "E", "E", "N", "S", "S", "W"], "observed_path_faces": [{"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C321_path_sequence.png"}, "metadata": {"level_id": 321, "name": "Reconstruct 321", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-321.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["O", "smile", "T", "X", "I", "diamond"], "start_x": 1, "start_y": 1, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "O", "rotation": 0}, "BOTTOM": {"patternId": "diamond", "rotation": 270}, "FRONT": {"patternId": "smile", "rotation": 270}, "BACK": {"patternId": "X", "rotation": 90}, "LEFT": {"patternId": "I", "rotation": 90}, "RIGHT": {"patternId": "T", "rotation": 270}}, "bottom_faces": [{"patternId": "diamond", "rotation": 270, "x": 1, "y": 1}, {"patternId": "smile", "rotation": 270, "x": 1, "y": 2}, {"patternId": "T", "rotation": 270, "x": 2, "y": 2}, {"patternId": "X", "rotation": 90, "x": 3, "y": 2}, {"patternId": "I", "rotation": 90, "x": 4, "y": 2}, {"patternId": "diamond", "rotation": 0, "x": 4, "y": 1}, {"patternId": "I", "rotation": 90, "x": 4, "y": 2}, {"patternId": "O", "rotation": 270, "x": 4, "y": 3}, {"patternId": "X", "rotation": 180, "x": 3, "y": 3}], "slot_sequence": ["FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM", "LEFT", "TOP", "BACK"], "required_slots": ["FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "O", "rotation": 0}, "BOTTOM": {"patternId": "diamond", "rotation": 270}, "FRONT": {"patternId": "smile", "rotation": 270}, "BACK": {"patternId": "X", "rotation": 270}, "LEFT": {"patternId": "I", "rotation": 180}, "RIGHT": {"patternId": "T", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 0}, "BOTTOM": {"patternId": "diamond", "rotation": 270}, "FRONT": {"patternId": "smile", "rotation": 270}, "BACK": {"patternId": "X", "rotation": 270}, "LEFT": {"patternId": "I", "rotation": 180}, "RIGHT": {"patternId": "T", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C321\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> E -> E -> N -> S -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=smile, rotation=270, flipVertical=true\n- step 2: patternId=T, rotation=270, flipVertical=true\n- step 3: patternId=X, rotation=90, flipVertical=true\n- step 4: patternId=I, rotation=90, flipVertical=true\n- step 5: patternId=diamond, rotation=0, flipVertical=true\n- step 6: patternId=I, rotation=90, flipVertical=true\n- step 7: patternId=O, rotation=270, flipVertical=true\n- step 8: patternId=X, rotation=180, flipVertical=true\n- allowed patternId values for this task: smile, T, X, I, diamond, O, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C321"} +{"sample_id": "C322", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> S -> W -> E -> W -> W -> S -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "S", "W", "E", "W", "W", "S", "N", "W"], "observed_path_faces": [{"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C322_path_sequence.png"}, "metadata": {"level_id": 322, "name": "Reconstruct 322", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-322.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["circle", "star", "heart", "B", "T", "J"], "start_x": 4, "start_y": 2, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "circle", "rotation": 0}, "BOTTOM": {"patternId": "J", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 270}, "LEFT": {"patternId": "T", "rotation": 90}, "RIGHT": {"patternId": "heart", "rotation": 90}}, "bottom_faces": [{"patternId": "J", "rotation": 0, "x": 4, "y": 2}, {"patternId": "B", "rotation": 90, "x": 4, "y": 1}, {"patternId": "J", "rotation": 0, "x": 4, "y": 2}, {"patternId": "T", "rotation": 0, "x": 3, "y": 2}, {"patternId": "J", "rotation": 0, "x": 4, "y": 2}, {"patternId": "T", "rotation": 0, "x": 3, "y": 2}, {"patternId": "circle", "rotation": 180, "x": 2, "y": 2}, {"patternId": "star", "rotation": 180, "x": 2, "y": 3}, {"patternId": "circle", "rotation": 180, "x": 2, "y": 2}, {"patternId": "heart", "rotation": 180, "x": 1, "y": 2}], "slot_sequence": ["BACK", "BOTTOM", "LEFT", "BOTTOM", "LEFT", "TOP", "FRONT", "TOP", "RIGHT"], "required_slots": ["BACK", "BOTTOM", "LEFT", "TOP", "FRONT", "RIGHT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "circle", "rotation": 0}, "BOTTOM": {"patternId": "J", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 90}, "LEFT": {"patternId": "T", "rotation": 180}, "RIGHT": {"patternId": "heart", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 0}, "BOTTOM": {"patternId": "J", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 90}, "LEFT": {"patternId": "T", "rotation": 180}, "RIGHT": {"patternId": "heart", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C322\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): N -> S -> W -> E -> W -> W -> S -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=B, rotation=90, flipVertical=true\n- step 2: patternId=J, rotation=0, flipVertical=true\n- step 3: patternId=T, rotation=0, flipVertical=true\n- step 4: patternId=J, rotation=0, flipVertical=true\n- step 5: patternId=T, rotation=0, flipVertical=true\n- step 6: patternId=circle, rotation=180, flipVertical=true\n- step 7: patternId=star, rotation=180, flipVertical=true\n- step 8: patternId=circle, rotation=180, flipVertical=true\n- step 9: patternId=heart, rotation=180, flipVertical=true\n- allowed patternId values for this task: B, J, T, circle, star, heart, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C322"} +{"sample_id": "C323", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> W -> W -> S -> S -> W -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "W", "W", "S", "S", "W", "W", "S"], "observed_path_faces": [{"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C323_path_sequence.png"}, "metadata": {"level_id": 323, "name": "Reconstruct 323", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-323.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_left", "P", "9", "arrow_down", "T", "D"], "start_x": 4, "start_y": 2, "grid_width": 7, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "arrow_left", "rotation": 270}, "BOTTOM": {"patternId": "D", "rotation": 180}, "FRONT": {"patternId": "P", "rotation": 180}, "BACK": {"patternId": "arrow_down", "rotation": 270}, "LEFT": {"patternId": "T", "rotation": 180}, "RIGHT": {"patternId": "9", "rotation": 90}}, "bottom_faces": [{"patternId": "D", "rotation": 180, "x": 4, "y": 2}, {"patternId": "9", "rotation": 180, "x": 5, "y": 2}, {"patternId": "arrow_down", "rotation": 0, "x": 5, "y": 1}, {"patternId": "D", "rotation": 90, "x": 4, "y": 1}, {"patternId": "P", "rotation": 90, "x": 3, "y": 1}, {"patternId": "9", "rotation": 0, "x": 3, "y": 2}, {"patternId": "arrow_down", "rotation": 180, "x": 3, "y": 3}, {"patternId": "arrow_left", "rotation": 0, "x": 2, "y": 3}, {"patternId": "P", "rotation": 270, "x": 1, "y": 3}, {"patternId": "T", "rotation": 270, "x": 1, "y": 4}], "slot_sequence": ["RIGHT", "BACK", "BOTTOM", "FRONT", "RIGHT", "BACK", "TOP", "FRONT", "LEFT"], "required_slots": ["RIGHT", "BACK", "BOTTOM", "FRONT", "TOP", "LEFT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "arrow_left", "rotation": 270}, "BOTTOM": {"patternId": "D", "rotation": 180}, "FRONT": {"patternId": "P", "rotation": 180}, "BACK": {"patternId": "arrow_down", "rotation": 90}, "LEFT": {"patternId": "T", "rotation": 270}, "RIGHT": {"patternId": "9", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "arrow_left", "rotation": 270}, "BOTTOM": {"patternId": "D", "rotation": 180}, "FRONT": {"patternId": "P", "rotation": 180}, "BACK": {"patternId": "arrow_down", "rotation": 90}, "LEFT": {"patternId": "T", "rotation": 270}, "RIGHT": {"patternId": "9", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C323\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> W -> W -> S -> S -> W -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=9, rotation=180, flipVertical=true\n- step 2: patternId=arrow_down, rotation=0, flipVertical=true\n- step 3: patternId=D, rotation=90, flipVertical=true\n- step 4: patternId=P, rotation=90, flipVertical=true\n- step 5: patternId=9, rotation=0, flipVertical=true\n- step 6: patternId=arrow_down, rotation=180, flipVertical=true\n- step 7: patternId=arrow_left, rotation=0, flipVertical=true\n- step 8: patternId=P, rotation=270, flipVertical=true\n- step 9: patternId=T, rotation=270, flipVertical=true\n- allowed patternId values for this task: 9, arrow_down, D, P, arrow_left, T, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C323"} +{"sample_id": "C324", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> S -> S -> W -> S -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "S", "S", "W", "S", "N", "W"], "observed_path_faces": [{"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C324_path_sequence.png"}, "metadata": {"level_id": 324, "name": "Reconstruct 324", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-324.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Z", "2", "Y", "L", "arrow_down", "W"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "Z", "rotation": 270}, "BOTTOM": {"patternId": "W", "rotation": 90}, "FRONT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "L", "rotation": 90}, "LEFT": {"patternId": "arrow_down", "rotation": 90}, "RIGHT": {"patternId": "Y", "rotation": 90}}, "bottom_faces": [{"patternId": "W", "rotation": 90, "x": 1, "y": 1}, {"patternId": "Y", "rotation": 180, "x": 2, "y": 1}, {"patternId": "Z", "rotation": 90, "x": 3, "y": 1}, {"patternId": "2", "rotation": 90, "x": 3, "y": 2}, {"patternId": "W", "rotation": 270, "x": 3, "y": 3}, {"patternId": "Y", "rotation": 0, "x": 2, "y": 3}, {"patternId": "L", "rotation": 0, "x": 2, "y": 4}, {"patternId": "Y", "rotation": 0, "x": 2, "y": 3}, {"patternId": "Z", "rotation": 270, "x": 1, "y": 3}], "slot_sequence": ["RIGHT", "TOP", "FRONT", "BOTTOM", "RIGHT", "BACK", "RIGHT", "TOP"], "required_slots": ["RIGHT", "TOP", "FRONT", "BOTTOM", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "Z", "rotation": 270}, "BOTTOM": {"patternId": "W", "rotation": 90}, "FRONT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "L", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Y", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "Z", "rotation": 270}, "BOTTOM": {"patternId": "W", "rotation": 90}, "FRONT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "L", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Y", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C324\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> S -> S -> W -> S -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Y, rotation=180, flipVertical=true\n- step 2: patternId=Z, rotation=90, flipVertical=true\n- step 3: patternId=2, rotation=90, flipVertical=true\n- step 4: patternId=W, rotation=270, flipVertical=true\n- step 5: patternId=Y, rotation=0, flipVertical=true\n- step 6: patternId=L, rotation=0, flipVertical=true\n- step 7: patternId=Y, rotation=0, flipVertical=true\n- step 8: patternId=Z, rotation=270, flipVertical=true\n- allowed patternId values for this task: Y, Z, 2, W, L, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C324"} +{"sample_id": "C325", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> E -> E -> E -> N -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "E", "E", "E", "N", "W", "S"], "observed_path_faces": [{"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C325_path_sequence.png"}, "metadata": {"level_id": 325, "name": "Reconstruct 325", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-325.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["M", "D", "I", "T", "S", "arrow_left"], "start_x": 1, "start_y": 1, "grid_width": 7, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "M", "rotation": 90}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 270}, "BACK": {"patternId": "T", "rotation": 0}, "LEFT": {"patternId": "S", "rotation": 270}, "RIGHT": {"patternId": "I", "rotation": 180}}, "bottom_faces": [{"patternId": "arrow_left", "rotation": 0, "x": 1, "y": 1}, {"patternId": "I", "rotation": 270, "x": 2, "y": 1}, {"patternId": "D", "rotation": 0, "x": 2, "y": 2}, {"patternId": "M", "rotation": 180, "x": 3, "y": 2}, {"patternId": "T", "rotation": 270, "x": 4, "y": 2}, {"patternId": "arrow_left", "rotation": 90, "x": 5, "y": 2}, {"patternId": "I", "rotation": 0, "x": 5, "y": 1}, {"patternId": "T", "rotation": 180, "x": 4, "y": 1}, {"patternId": "arrow_left", "rotation": 0, "x": 4, "y": 2}], "slot_sequence": ["RIGHT", "FRONT", "TOP", "BACK", "BOTTOM", "RIGHT", "BACK", "BOTTOM"], "required_slots": ["RIGHT", "FRONT", "TOP", "BACK", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "M", "rotation": 90}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 270}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 90}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 270}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C325\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> E -> E -> E -> N -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=I, rotation=270, flipVertical=true\n- step 2: patternId=D, rotation=0, flipVertical=true\n- step 3: patternId=M, rotation=180, flipVertical=true\n- step 4: patternId=T, rotation=270, flipVertical=true\n- step 5: patternId=arrow_left, rotation=90, flipVertical=true\n- step 6: patternId=I, rotation=0, flipVertical=true\n- step 7: patternId=T, rotation=180, flipVertical=true\n- step 8: patternId=arrow_left, rotation=0, flipVertical=true\n- allowed patternId values for this task: I, D, M, T, arrow_left, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C325"} +{"sample_id": "C326", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> S -> E -> N -> E -> N -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "S", "E", "N", "E", "N", "E", "N"], "observed_path_faces": [{"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C326_path_sequence.png"}, "metadata": {"level_id": 326, "name": "Reconstruct 326", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-326.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["4", "M", "I", "star", "O", "diamond"], "start_x": 1, "start_y": 2, "grid_width": 7, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "4", "rotation": 90}, "BOTTOM": {"patternId": "diamond", "rotation": 180}, "FRONT": {"patternId": "M", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 180}, "LEFT": {"patternId": "O", "rotation": 180}, "RIGHT": {"patternId": "I", "rotation": 90}}, "bottom_faces": [{"patternId": "diamond", "rotation": 180, "x": 1, "y": 2}, {"patternId": "I", "rotation": 180, "x": 2, "y": 2}, {"patternId": "M", "rotation": 90, "x": 2, "y": 3}, {"patternId": "O", "rotation": 270, "x": 2, "y": 4}, {"patternId": "4", "rotation": 90, "x": 3, "y": 4}, {"patternId": "M", "rotation": 0, "x": 3, "y": 3}, {"patternId": "I", "rotation": 90, "x": 4, "y": 3}, {"patternId": "diamond", "rotation": 90, "x": 4, "y": 2}, {"patternId": "star", "rotation": 270, "x": 5, "y": 2}, {"patternId": "O", "rotation": 270, "x": 5, "y": 1}], "slot_sequence": ["RIGHT", "FRONT", "LEFT", "TOP", "FRONT", "RIGHT", "BOTTOM", "BACK", "LEFT"], "required_slots": ["RIGHT", "FRONT", "LEFT", "TOP", "BOTTOM", "BACK"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "4", "rotation": 90}, "BOTTOM": {"patternId": "diamond", "rotation": 180}, "FRONT": {"patternId": "M", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 270}, "RIGHT": {"patternId": "I", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "4", "rotation": 90}, "BOTTOM": {"patternId": "diamond", "rotation": 180}, "FRONT": {"patternId": "M", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 270}, "RIGHT": {"patternId": "I", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C326\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> S -> E -> N -> E -> N -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=I, rotation=180, flipVertical=true\n- step 2: patternId=M, rotation=90, flipVertical=true\n- step 3: patternId=O, rotation=270, flipVertical=true\n- step 4: patternId=4, rotation=90, flipVertical=true\n- step 5: patternId=M, rotation=0, flipVertical=true\n- step 6: patternId=I, rotation=90, flipVertical=true\n- step 7: patternId=diamond, rotation=90, flipVertical=true\n- step 8: patternId=star, rotation=270, flipVertical=true\n- step 9: patternId=O, rotation=270, flipVertical=true\n- allowed patternId values for this task: I, M, O, 4, diamond, star, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C326"} +{"sample_id": "C327", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> E -> N -> E -> W -> S -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "E", "N", "E", "W", "S", "S", "E"], "observed_path_faces": [{"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C327_path_sequence.png"}, "metadata": {"level_id": 327, "name": "Reconstruct 327", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-327.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["G", "C", "V", "H", "X", "arrow_right"], "start_x": 1, "start_y": 3, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "G", "rotation": 0}, "BOTTOM": {"patternId": "arrow_right", "rotation": 180}, "FRONT": {"patternId": "C", "rotation": 270}, "BACK": {"patternId": "H", "rotation": 0}, "LEFT": {"patternId": "X", "rotation": 270}, "RIGHT": {"patternId": "V", "rotation": 180}}, "bottom_faces": [{"patternId": "arrow_right", "rotation": 180, "x": 1, "y": 3}, {"patternId": "V", "rotation": 270, "x": 2, "y": 3}, {"patternId": "H", "rotation": 90, "x": 2, "y": 2}, {"patternId": "G", "rotation": 270, "x": 3, "y": 2}, {"patternId": "X", "rotation": 270, "x": 3, "y": 1}, {"patternId": "C", "rotation": 270, "x": 4, "y": 1}, {"patternId": "X", "rotation": 270, "x": 3, "y": 1}, {"patternId": "G", "rotation": 270, "x": 3, "y": 2}, {"patternId": "V", "rotation": 0, "x": 3, "y": 3}, {"patternId": "C", "rotation": 90, "x": 4, "y": 3}], "slot_sequence": ["RIGHT", "BACK", "TOP", "LEFT", "FRONT", "LEFT", "TOP", "RIGHT", "FRONT"], "required_slots": ["RIGHT", "BACK", "TOP", "LEFT", "FRONT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "G", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "C", "rotation": 270}, "BACK": {"patternId": "H", "rotation": 180}, "LEFT": {"patternId": "X", "rotation": 0}, "RIGHT": {"patternId": "V", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "G", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "C", "rotation": 270}, "BACK": {"patternId": "H", "rotation": 180}, "LEFT": {"patternId": "X", "rotation": 0}, "RIGHT": {"patternId": "V", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C327\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> E -> N -> E -> W -> S -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=V, rotation=270, flipVertical=true\n- step 2: patternId=H, rotation=90, flipVertical=true\n- step 3: patternId=G, rotation=270, flipVertical=true\n- step 4: patternId=X, rotation=270, flipVertical=true\n- step 5: patternId=C, rotation=270, flipVertical=true\n- step 6: patternId=X, rotation=270, flipVertical=true\n- step 7: patternId=G, rotation=270, flipVertical=true\n- step 8: patternId=V, rotation=0, flipVertical=true\n- step 9: patternId=C, rotation=90, flipVertical=true\n- allowed patternId values for this task: V, H, G, X, C, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C327"} +{"sample_id": "C328", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> S -> W -> W -> E -> S -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "S", "W", "W", "E", "S", "W", "W"], "observed_path_faces": [{"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C328_path_sequence.png"}, "metadata": {"level_id": 328, "name": "Reconstruct 328", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-328.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["K", "F", "M", "plus", "8", "8"], "start_x": 3, "start_y": 1, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "K", "rotation": 90}, "BOTTOM": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "F", "rotation": 0}, "BACK": {"patternId": "plus", "rotation": 180}, "LEFT": {"patternId": "8", "rotation": 90}, "RIGHT": {"patternId": "M", "rotation": 180}}, "bottom_faces": [{"patternId": "8", "rotation": 180, "x": 3, "y": 1}, {"patternId": "F", "rotation": 0, "x": 3, "y": 2}, {"patternId": "M", "rotation": 180, "x": 4, "y": 2}, {"patternId": "K", "rotation": 180, "x": 4, "y": 3}, {"patternId": "F", "rotation": 90, "x": 3, "y": 3}, {"patternId": "8", "rotation": 270, "x": 2, "y": 3}, {"patternId": "F", "rotation": 90, "x": 3, "y": 3}, {"patternId": "8", "rotation": 180, "x": 3, "y": 4}, {"patternId": "8", "rotation": 0, "x": 2, "y": 4}, {"patternId": "M", "rotation": 90, "x": 1, "y": 4}], "slot_sequence": ["FRONT", "RIGHT", "TOP", "FRONT", "BOTTOM", "FRONT", "LEFT", "BOTTOM", "RIGHT"], "required_slots": ["FRONT", "RIGHT", "TOP", "BOTTOM", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "K", "rotation": 90}, "BOTTOM": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "F", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 180}, "RIGHT": {"patternId": "M", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "K", "rotation": 90}, "BOTTOM": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "F", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 180}, "RIGHT": {"patternId": "M", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C328\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> S -> W -> W -> E -> S -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=F, rotation=0, flipVertical=true\n- step 2: patternId=M, rotation=180, flipVertical=true\n- step 3: patternId=K, rotation=180, flipVertical=true\n- step 4: patternId=F, rotation=90, flipVertical=true\n- step 5: patternId=8, rotation=270, flipVertical=true\n- step 6: patternId=F, rotation=90, flipVertical=true\n- step 7: patternId=8, rotation=180, flipVertical=true\n- step 8: patternId=8, rotation=0, flipVertical=true\n- step 9: patternId=M, rotation=90, flipVertical=true\n- allowed patternId values for this task: F, M, K, 8, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C328"} +{"sample_id": "C329", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> W -> S -> W -> S -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "W", "S", "W", "S", "S", "S"], "observed_path_faces": [{"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C329_path_sequence.png"}, "metadata": {"level_id": 329, "name": "Reconstruct 329", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-329.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_right", "square", "circle", "T", "arrow_down", "arrow_left"], "start_x": 4, "start_y": 1, "grid_width": 6, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "arrow_right", "rotation": 0}, "BOTTOM": {"patternId": "arrow_left", "rotation": 90}, "FRONT": {"patternId": "square", "rotation": 90}, "BACK": {"patternId": "T", "rotation": 0}, "LEFT": {"patternId": "arrow_down", "rotation": 180}, "RIGHT": {"patternId": "circle", "rotation": 0}}, "bottom_faces": [{"patternId": "arrow_left", "rotation": 90, "x": 4, "y": 1}, {"patternId": "square", "rotation": 90, "x": 4, "y": 2}, {"patternId": "arrow_down", "rotation": 180, "x": 3, "y": 2}, {"patternId": "T", "rotation": 0, "x": 2, "y": 2}, {"patternId": "arrow_right", "rotation": 180, "x": 2, "y": 3}, {"patternId": "circle", "rotation": 90, "x": 1, "y": 3}, {"patternId": "square", "rotation": 180, "x": 1, "y": 4}, {"patternId": "arrow_down", "rotation": 270, "x": 1, "y": 5}, {"patternId": "T", "rotation": 90, "x": 1, "y": 6}], "slot_sequence": ["FRONT", "LEFT", "BACK", "TOP", "RIGHT", "FRONT", "LEFT", "BACK"], "required_slots": ["FRONT", "LEFT", "BACK", "TOP", "RIGHT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "arrow_right", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 90}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "arrow_down", "rotation": 270}, "RIGHT": {"patternId": "circle", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "arrow_right", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 90}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "arrow_down", "rotation": 270}, "RIGHT": {"patternId": "circle", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C329\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> W -> S -> W -> S -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=square, rotation=90, flipVertical=true\n- step 2: patternId=arrow_down, rotation=180, flipVertical=true\n- step 3: patternId=T, rotation=0, flipVertical=true\n- step 4: patternId=arrow_right, rotation=180, flipVertical=true\n- step 5: patternId=circle, rotation=90, flipVertical=true\n- step 6: patternId=square, rotation=180, flipVertical=true\n- step 7: patternId=arrow_down, rotation=270, flipVertical=true\n- step 8: patternId=T, rotation=90, flipVertical=true\n- allowed patternId values for this task: square, arrow_down, T, arrow_right, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C329"} +{"sample_id": "C330", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> N -> W -> W -> N -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "N", "W", "W", "N", "E", "N"], "observed_path_faces": [{"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C330_path_sequence.png"}, "metadata": {"level_id": 330, "name": "Reconstruct 330", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-330.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["S", "T", "G", "J", "W", "T"], "start_x": 4, "start_y": 5, "grid_width": 6, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "S", "rotation": 180}, "BOTTOM": {"patternId": "T", "rotation": 90}, "FRONT": {"patternId": "T", "rotation": 270}, "BACK": {"patternId": "J", "rotation": 270}, "LEFT": {"patternId": "W", "rotation": 0}, "RIGHT": {"patternId": "G", "rotation": 180}}, "bottom_faces": [{"patternId": "T", "rotation": 90, "x": 4, "y": 5}, {"patternId": "W", "rotation": 270, "x": 3, "y": 5}, {"patternId": "J", "rotation": 180, "x": 3, "y": 4}, {"patternId": "G", "rotation": 90, "x": 3, "y": 3}, {"patternId": "S", "rotation": 180, "x": 2, "y": 3}, {"patternId": "W", "rotation": 90, "x": 1, "y": 3}, {"patternId": "T", "rotation": 0, "x": 1, "y": 2}, {"patternId": "S", "rotation": 270, "x": 2, "y": 2}, {"patternId": "G", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["LEFT", "BACK", "RIGHT", "TOP", "LEFT", "FRONT", "TOP", "RIGHT"], "required_slots": ["LEFT", "BACK", "RIGHT", "TOP", "FRONT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "S", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "T", "rotation": 270}, "BACK": {"patternId": "J", "rotation": 90}, "LEFT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "G", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "T", "rotation": 270}, "BACK": {"patternId": "J", "rotation": 90}, "LEFT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "G", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C330\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> N -> W -> W -> N -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=W, rotation=270, flipVertical=true\n- step 2: patternId=J, rotation=180, flipVertical=true\n- step 3: patternId=G, rotation=90, flipVertical=true\n- step 4: patternId=S, rotation=180, flipVertical=true\n- step 5: patternId=W, rotation=90, flipVertical=true\n- step 6: patternId=T, rotation=0, flipVertical=true\n- step 7: patternId=S, rotation=270, flipVertical=true\n- step 8: patternId=G, rotation=180, flipVertical=true\n- allowed patternId values for this task: W, J, G, S, T, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C330"} +{"sample_id": "C331", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> N -> N -> N -> E -> N -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "N", "N", "N", "E", "N", "E", "N"], "observed_path_faces": [{"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C331_path_sequence.png"}, "metadata": {"level_id": 331, "name": "Reconstruct 331", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-331.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["E", "2", "B", "1", "S", "arrow_right"], "start_x": 1, "start_y": 5, "grid_width": 6, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "E", "rotation": 270}, "BOTTOM": {"patternId": "arrow_right", "rotation": 180}, "FRONT": {"patternId": "2", "rotation": 90}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "S", "rotation": 0}, "RIGHT": {"patternId": "B", "rotation": 90}}, "bottom_faces": [{"patternId": "arrow_right", "rotation": 180, "x": 1, "y": 5}, {"patternId": "2", "rotation": 90, "x": 1, "y": 6}, {"patternId": "B", "rotation": 90, "x": 2, "y": 6}, {"patternId": "arrow_right", "rotation": 90, "x": 2, "y": 5}, {"patternId": "S", "rotation": 180, "x": 2, "y": 4}, {"patternId": "E", "rotation": 0, "x": 2, "y": 3}, {"patternId": "1", "rotation": 90, "x": 3, "y": 3}, {"patternId": "B", "rotation": 0, "x": 3, "y": 2}, {"patternId": "arrow_right", "rotation": 0, "x": 4, "y": 2}, {"patternId": "2", "rotation": 270, "x": 4, "y": 1}], "slot_sequence": ["FRONT", "RIGHT", "BOTTOM", "LEFT", "TOP", "BACK", "RIGHT", "BOTTOM", "FRONT"], "required_slots": ["FRONT", "RIGHT", "BOTTOM", "LEFT", "TOP", "BACK"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "E", "rotation": 270}, "BOTTOM": {"patternId": "arrow_right", "rotation": 180}, "FRONT": {"patternId": "2", "rotation": 90}, "BACK": {"patternId": "1", "rotation": 0}, "LEFT": {"patternId": "S", "rotation": 90}, "RIGHT": {"patternId": "B", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "E", "rotation": 270}, "BOTTOM": {"patternId": "arrow_right", "rotation": 180}, "FRONT": {"patternId": "2", "rotation": 90}, "BACK": {"patternId": "1", "rotation": 0}, "LEFT": {"patternId": "S", "rotation": 90}, "RIGHT": {"patternId": "B", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C331\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> N -> N -> N -> E -> N -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=2, rotation=90, flipVertical=true\n- step 2: patternId=B, rotation=90, flipVertical=true\n- step 3: patternId=arrow_right, rotation=90, flipVertical=true\n- step 4: patternId=S, rotation=180, flipVertical=true\n- step 5: patternId=E, rotation=0, flipVertical=true\n- step 6: patternId=1, rotation=90, flipVertical=true\n- step 7: patternId=B, rotation=0, flipVertical=true\n- step 8: patternId=arrow_right, rotation=0, flipVertical=true\n- step 9: patternId=2, rotation=270, flipVertical=true\n- allowed patternId values for this task: 2, B, arrow_right, S, E, 1, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C331"} +{"sample_id": "C332", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> N -> W -> E -> E -> N -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "N", "W", "E", "E", "N", "N", "W"], "observed_path_faces": [{"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C332_path_sequence.png"}, "metadata": {"level_id": 332, "name": "Reconstruct 332", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-332.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["N", "T", "O", "diamond", "square", "Y"], "start_x": 3, "start_y": 5, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "N", "rotation": 0}, "BOTTOM": {"patternId": "Y", "rotation": 90}, "FRONT": {"patternId": "T", "rotation": 90}, "BACK": {"patternId": "diamond", "rotation": 270}, "LEFT": {"patternId": "square", "rotation": 90}, "RIGHT": {"patternId": "O", "rotation": 90}}, "bottom_faces": [{"patternId": "Y", "rotation": 90, "x": 3, "y": 5}, {"patternId": "square", "rotation": 0, "x": 2, "y": 5}, {"patternId": "diamond", "rotation": 180, "x": 2, "y": 4}, {"patternId": "O", "rotation": 0, "x": 2, "y": 3}, {"patternId": "N", "rotation": 0, "x": 1, "y": 3}, {"patternId": "O", "rotation": 0, "x": 2, "y": 3}, {"patternId": "Y", "rotation": 270, "x": 3, "y": 3}, {"patternId": "T", "rotation": 270, "x": 3, "y": 2}, {"patternId": "N", "rotation": 180, "x": 3, "y": 1}, {"patternId": "O", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["LEFT", "BACK", "RIGHT", "TOP", "RIGHT", "BOTTOM", "FRONT", "TOP", "RIGHT"], "required_slots": ["LEFT", "BACK", "RIGHT", "TOP", "BOTTOM", "FRONT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "N", "rotation": 0}, "BOTTOM": {"patternId": "Y", "rotation": 90}, "FRONT": {"patternId": "T", "rotation": 90}, "BACK": {"patternId": "diamond", "rotation": 90}, "LEFT": {"patternId": "square", "rotation": 180}, "RIGHT": {"patternId": "O", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "N", "rotation": 0}, "BOTTOM": {"patternId": "Y", "rotation": 90}, "FRONT": {"patternId": "T", "rotation": 90}, "BACK": {"patternId": "diamond", "rotation": 90}, "LEFT": {"patternId": "square", "rotation": 180}, "RIGHT": {"patternId": "O", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C332\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> N -> W -> E -> E -> N -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=square, rotation=0, flipVertical=true\n- step 2: patternId=diamond, rotation=180, flipVertical=true\n- step 3: patternId=O, rotation=0, flipVertical=true\n- step 4: patternId=N, rotation=0, flipVertical=true\n- step 5: patternId=O, rotation=0, flipVertical=true\n- step 6: patternId=Y, rotation=270, flipVertical=true\n- step 7: patternId=T, rotation=270, flipVertical=true\n- step 8: patternId=N, rotation=180, flipVertical=true\n- step 9: patternId=O, rotation=180, flipVertical=true\n- allowed patternId values for this task: square, diamond, O, N, Y, T, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C332"} +{"sample_id": "C333", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> E -> W -> N -> N -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "E", "W", "N", "N", "E", "E"], "observed_path_faces": [{"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C333_path_sequence.png"}, "metadata": {"level_id": 333, "name": "Reconstruct 333", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-333.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["N", "A", "7", "8", "diamond", "6"], "start_x": 1, "start_y": 2, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "N", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 0}, "FRONT": {"patternId": "A", "rotation": 180}, "BACK": {"patternId": "8", "rotation": 270}, "LEFT": {"patternId": "diamond", "rotation": 90}, "RIGHT": {"patternId": "7", "rotation": 0}}, "bottom_faces": [{"patternId": "6", "rotation": 0, "x": 1, "y": 2}, {"patternId": "A", "rotation": 180, "x": 1, "y": 3}, {"patternId": "7", "rotation": 0, "x": 2, "y": 3}, {"patternId": "8", "rotation": 270, "x": 3, "y": 3}, {"patternId": "7", "rotation": 0, "x": 2, "y": 3}, {"patternId": "6", "rotation": 270, "x": 2, "y": 2}, {"patternId": "diamond", "rotation": 270, "x": 2, "y": 1}, {"patternId": "8", "rotation": 90, "x": 3, "y": 1}, {"patternId": "7", "rotation": 180, "x": 4, "y": 1}], "slot_sequence": ["FRONT", "RIGHT", "BACK", "RIGHT", "BOTTOM", "LEFT", "BACK", "RIGHT"], "required_slots": ["FRONT", "RIGHT", "BACK", "BOTTOM", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 0}, "FRONT": {"patternId": "A", "rotation": 180}, "BACK": {"patternId": "8", "rotation": 90}, "LEFT": {"patternId": "diamond", "rotation": 180}, "RIGHT": {"patternId": "7", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 0}, "FRONT": {"patternId": "A", "rotation": 180}, "BACK": {"patternId": "8", "rotation": 90}, "LEFT": {"patternId": "diamond", "rotation": 180}, "RIGHT": {"patternId": "7", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C333\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> E -> W -> N -> N -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=A, rotation=180, flipVertical=true\n- step 2: patternId=7, rotation=0, flipVertical=true\n- step 3: patternId=8, rotation=270, flipVertical=true\n- step 4: patternId=7, rotation=0, flipVertical=true\n- step 5: patternId=6, rotation=270, flipVertical=true\n- step 6: patternId=diamond, rotation=270, flipVertical=true\n- step 7: patternId=8, rotation=90, flipVertical=true\n- step 8: patternId=7, rotation=180, flipVertical=true\n- allowed patternId values for this task: A, 7, 8, 6, diamond, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C333"} +{"sample_id": "C334", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> N -> W -> N -> W -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "N", "W", "N", "W", "W", "S"], "observed_path_faces": [{"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C334_path_sequence.png"}, "metadata": {"level_id": 334, "name": "Reconstruct 334", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-334.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["O", "O", "Q", "circle", "smile", "V"], "start_x": 3, "start_y": 2, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "O", "rotation": 180}, "BOTTOM": {"patternId": "V", "rotation": 180}, "FRONT": {"patternId": "O", "rotation": 180}, "BACK": {"patternId": "circle", "rotation": 180}, "LEFT": {"patternId": "smile", "rotation": 270}, "RIGHT": {"patternId": "Q", "rotation": 180}}, "bottom_faces": [{"patternId": "V", "rotation": 180, "x": 3, "y": 2}, {"patternId": "O", "rotation": 180, "x": 3, "y": 3}, {"patternId": "Q", "rotation": 180, "x": 4, "y": 3}, {"patternId": "V", "rotation": 90, "x": 4, "y": 2}, {"patternId": "O", "rotation": 90, "x": 3, "y": 2}, {"patternId": "smile", "rotation": 180, "x": 3, "y": 1}, {"patternId": "O", "rotation": 0, "x": 2, "y": 1}, {"patternId": "Q", "rotation": 270, "x": 1, "y": 1}, {"patternId": "O", "rotation": 270, "x": 1, "y": 2}], "slot_sequence": ["FRONT", "RIGHT", "BOTTOM", "FRONT", "LEFT", "TOP", "RIGHT", "FRONT"], "required_slots": ["FRONT", "RIGHT", "BOTTOM", "LEFT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "O", "rotation": 180}, "BOTTOM": {"patternId": "V", "rotation": 180}, "FRONT": {"patternId": "O", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "smile", "rotation": 0}, "RIGHT": {"patternId": "Q", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 180}, "BOTTOM": {"patternId": "V", "rotation": 180}, "FRONT": {"patternId": "O", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "smile", "rotation": 0}, "RIGHT": {"patternId": "Q", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C334\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> N -> W -> N -> W -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=O, rotation=180, flipVertical=true\n- step 2: patternId=Q, rotation=180, flipVertical=true\n- step 3: patternId=V, rotation=90, flipVertical=true\n- step 4: patternId=O, rotation=90, flipVertical=true\n- step 5: patternId=smile, rotation=180, flipVertical=true\n- step 6: patternId=O, rotation=0, flipVertical=true\n- step 7: patternId=Q, rotation=270, flipVertical=true\n- step 8: patternId=O, rotation=270, flipVertical=true\n- allowed patternId values for this task: O, Q, V, smile, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C334"} +{"sample_id": "C335", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> W -> S -> E -> S -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "W", "S", "E", "S", "W", "S"], "observed_path_faces": [{"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C335_path_sequence.png"}, "metadata": {"level_id": 335, "name": "Reconstruct 335", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-335.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["I", "6", "4", "circle", "C", "M"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "I", "rotation": 90}, "BOTTOM": {"patternId": "M", "rotation": 90}, "FRONT": {"patternId": "6", "rotation": 270}, "BACK": {"patternId": "circle", "rotation": 180}, "LEFT": {"patternId": "C", "rotation": 0}, "RIGHT": {"patternId": "4", "rotation": 90}}, "bottom_faces": [{"patternId": "M", "rotation": 90, "x": 3, "y": 1}, {"patternId": "6", "rotation": 270, "x": 3, "y": 2}, {"patternId": "C", "rotation": 0, "x": 2, "y": 2}, {"patternId": "circle", "rotation": 180, "x": 1, "y": 2}, {"patternId": "I", "rotation": 270, "x": 1, "y": 3}, {"patternId": "C", "rotation": 270, "x": 2, "y": 3}, {"patternId": "6", "rotation": 180, "x": 2, "y": 4}, {"patternId": "I", "rotation": 0, "x": 1, "y": 4}, {"patternId": "4", "rotation": 270, "x": 1, "y": 5}], "slot_sequence": ["FRONT", "LEFT", "BACK", "TOP", "LEFT", "FRONT", "TOP", "RIGHT"], "required_slots": ["FRONT", "LEFT", "BACK", "TOP", "RIGHT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "I", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "6", "rotation": 270}, "BACK": {"patternId": "circle", "rotation": 0}, "LEFT": {"patternId": "C", "rotation": 90}, "RIGHT": {"patternId": "4", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "6", "rotation": 270}, "BACK": {"patternId": "circle", "rotation": 0}, "LEFT": {"patternId": "C", "rotation": 90}, "RIGHT": {"patternId": "4", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C335\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> W -> S -> E -> S -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=6, rotation=270, flipVertical=true\n- step 2: patternId=C, rotation=0, flipVertical=true\n- step 3: patternId=circle, rotation=180, flipVertical=true\n- step 4: patternId=I, rotation=270, flipVertical=true\n- step 5: patternId=C, rotation=270, flipVertical=true\n- step 6: patternId=6, rotation=180, flipVertical=true\n- step 7: patternId=I, rotation=0, flipVertical=true\n- step 8: patternId=4, rotation=270, flipVertical=true\n- allowed patternId values for this task: 6, C, circle, I, 4, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C335"} +{"sample_id": "C336", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> W -> N -> N -> W -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "W", "N", "N", "W", "N", "E"], "observed_path_faces": [{"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C336_path_sequence.png"}, "metadata": {"level_id": 336, "name": "Reconstruct 336", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-336.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["C", "4", "circle", "3", "D", "L"], "start_x": 3, "start_y": 2, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "C", "rotation": 180}, "BOTTOM": {"patternId": "L", "rotation": 0}, "FRONT": {"patternId": "4", "rotation": 270}, "BACK": {"patternId": "3", "rotation": 270}, "LEFT": {"patternId": "D", "rotation": 270}, "RIGHT": {"patternId": "circle", "rotation": 0}}, "bottom_faces": [{"patternId": "L", "rotation": 0, "x": 3, "y": 2}, {"patternId": "4", "rotation": 270, "x": 3, "y": 3}, {"patternId": "C", "rotation": 180, "x": 3, "y": 4}, {"patternId": "D", "rotation": 0, "x": 2, "y": 4}, {"patternId": "4", "rotation": 0, "x": 2, "y": 3}, {"patternId": "circle", "rotation": 90, "x": 2, "y": 2}, {"patternId": "L", "rotation": 0, "x": 1, "y": 2}, {"patternId": "3", "rotation": 90, "x": 1, "y": 1}, {"patternId": "circle", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["FRONT", "TOP", "LEFT", "FRONT", "RIGHT", "BOTTOM", "BACK", "RIGHT"], "required_slots": ["FRONT", "TOP", "LEFT", "RIGHT", "BOTTOM", "BACK"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "C", "rotation": 180}, "BOTTOM": {"patternId": "L", "rotation": 0}, "FRONT": {"patternId": "4", "rotation": 270}, "BACK": {"patternId": "3", "rotation": 90}, "LEFT": {"patternId": "D", "rotation": 0}, "RIGHT": {"patternId": "circle", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "C", "rotation": 180}, "BOTTOM": {"patternId": "L", "rotation": 0}, "FRONT": {"patternId": "4", "rotation": 270}, "BACK": {"patternId": "3", "rotation": 90}, "LEFT": {"patternId": "D", "rotation": 0}, "RIGHT": {"patternId": "circle", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C336\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> W -> N -> N -> W -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=4, rotation=270, flipVertical=true\n- step 2: patternId=C, rotation=180, flipVertical=true\n- step 3: patternId=D, rotation=0, flipVertical=true\n- step 4: patternId=4, rotation=0, flipVertical=true\n- step 5: patternId=circle, rotation=90, flipVertical=true\n- step 6: patternId=L, rotation=0, flipVertical=true\n- step 7: patternId=3, rotation=90, flipVertical=true\n- step 8: patternId=circle, rotation=180, flipVertical=true\n- allowed patternId values for this task: 4, C, D, circle, L, 3, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C336"} +{"sample_id": "C337", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> W -> E -> W -> S -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "W", "E", "W", "S", "S", "S"], "observed_path_faces": [{"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C337_path_sequence.png"}, "metadata": {"level_id": 337, "name": "Reconstruct 337", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-337.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["plus", "6", "O", "triangle", "M", "K"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "plus", "rotation": 270}, "BOTTOM": {"patternId": "K", "rotation": 0}, "FRONT": {"patternId": "6", "rotation": 270}, "BACK": {"patternId": "triangle", "rotation": 90}, "LEFT": {"patternId": "M", "rotation": 270}, "RIGHT": {"patternId": "O", "rotation": 180}}, "bottom_faces": [{"patternId": "K", "rotation": 0, "x": 1, "y": 1}, {"patternId": "6", "rotation": 270, "x": 1, "y": 2}, {"patternId": "O", "rotation": 180, "x": 2, "y": 2}, {"patternId": "6", "rotation": 270, "x": 1, "y": 2}, {"patternId": "O", "rotation": 180, "x": 2, "y": 2}, {"patternId": "6", "rotation": 270, "x": 1, "y": 2}, {"patternId": "plus", "rotation": 270, "x": 1, "y": 3}, {"patternId": "triangle", "rotation": 270, "x": 1, "y": 4}, {"patternId": "K", "rotation": 0, "x": 1, "y": 5}], "slot_sequence": ["FRONT", "RIGHT", "FRONT", "RIGHT", "FRONT", "TOP", "BACK", "BOTTOM"], "required_slots": ["FRONT", "RIGHT", "TOP", "BACK", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "plus", "rotation": 270}, "BOTTOM": {"patternId": "K", "rotation": 0}, "FRONT": {"patternId": "6", "rotation": 270}, "BACK": {"patternId": "triangle", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "plus", "rotation": 270}, "BOTTOM": {"patternId": "K", "rotation": 0}, "FRONT": {"patternId": "6", "rotation": 270}, "BACK": {"patternId": "triangle", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C337\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> W -> E -> W -> S -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=6, rotation=270, flipVertical=true\n- step 2: patternId=O, rotation=180, flipVertical=true\n- step 3: patternId=6, rotation=270, flipVertical=true\n- step 4: patternId=O, rotation=180, flipVertical=true\n- step 5: patternId=6, rotation=270, flipVertical=true\n- step 6: patternId=plus, rotation=270, flipVertical=true\n- step 7: patternId=triangle, rotation=270, flipVertical=true\n- step 8: patternId=K, rotation=0, flipVertical=true\n- allowed patternId values for this task: 6, O, plus, triangle, K, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C337"} +{"sample_id": "C338", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> W -> N -> W -> W -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "W", "N", "W", "W", "W", "N"], "observed_path_faces": [{"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C338_path_sequence.png"}, "metadata": {"level_id": 338, "name": "Reconstruct 338", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-338.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["4", "L", "5", "I", "8", "H"], "start_x": 7, "start_y": 3, "grid_width": 9, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "4", "rotation": 0}, "BOTTOM": {"patternId": "H", "rotation": 90}, "FRONT": {"patternId": "L", "rotation": 270}, "BACK": {"patternId": "I", "rotation": 90}, "LEFT": {"patternId": "8", "rotation": 270}, "RIGHT": {"patternId": "5", "rotation": 270}}, "bottom_faces": [{"patternId": "H", "rotation": 90, "x": 7, "y": 3}, {"patternId": "8", "rotation": 180, "x": 6, "y": 3}, {"patternId": "4", "rotation": 180, "x": 5, "y": 3}, {"patternId": "5", "rotation": 0, "x": 4, "y": 3}, {"patternId": "I", "rotation": 180, "x": 4, "y": 2}, {"patternId": "H", "rotation": 0, "x": 3, "y": 2}, {"patternId": "L", "rotation": 180, "x": 2, "y": 2}, {"patternId": "4", "rotation": 270, "x": 1, "y": 2}, {"patternId": "8", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "TOP", "RIGHT", "BACK", "BOTTOM", "FRONT", "TOP", "LEFT"], "required_slots": ["LEFT", "TOP", "RIGHT", "BACK", "BOTTOM", "FRONT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "4", "rotation": 0}, "BOTTOM": {"patternId": "H", "rotation": 90}, "FRONT": {"patternId": "L", "rotation": 270}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "8", "rotation": 0}, "RIGHT": {"patternId": "5", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "4", "rotation": 0}, "BOTTOM": {"patternId": "H", "rotation": 90}, "FRONT": {"patternId": "L", "rotation": 270}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "8", "rotation": 0}, "RIGHT": {"patternId": "5", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C338\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> W -> N -> W -> W -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=8, rotation=180, flipVertical=true\n- step 2: patternId=4, rotation=180, flipVertical=true\n- step 3: patternId=5, rotation=0, flipVertical=true\n- step 4: patternId=I, rotation=180, flipVertical=true\n- step 5: patternId=H, rotation=0, flipVertical=true\n- step 6: patternId=L, rotation=180, flipVertical=true\n- step 7: patternId=4, rotation=270, flipVertical=true\n- step 8: patternId=8, rotation=270, flipVertical=true\n- allowed patternId values for this task: 8, 4, 5, I, H, L, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C338"} +{"sample_id": "C339", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> E -> N -> E -> N -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "E", "N", "E", "N", "E", "S"], "observed_path_faces": [{"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C339_path_sequence.png"}, "metadata": {"level_id": 339, "name": "Reconstruct 339", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-339.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["N", "D", "A", "smile", "F", "U"], "start_x": 2, "start_y": 4, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "N", "rotation": 180}, "BOTTOM": {"patternId": "U", "rotation": 180}, "FRONT": {"patternId": "D", "rotation": 90}, "BACK": {"patternId": "smile", "rotation": 0}, "LEFT": {"patternId": "F", "rotation": 270}, "RIGHT": {"patternId": "A", "rotation": 0}}, "bottom_faces": [{"patternId": "U", "rotation": 180, "x": 2, "y": 4}, {"patternId": "F", "rotation": 180, "x": 1, "y": 4}, {"patternId": "smile", "rotation": 270, "x": 1, "y": 3}, {"patternId": "U", "rotation": 270, "x": 2, "y": 3}, {"patternId": "A", "rotation": 180, "x": 2, "y": 2}, {"patternId": "D", "rotation": 270, "x": 3, "y": 2}, {"patternId": "N", "rotation": 0, "x": 3, "y": 1}, {"patternId": "F", "rotation": 180, "x": 4, "y": 1}, {"patternId": "D", "rotation": 0, "x": 4, "y": 2}], "slot_sequence": ["LEFT", "BACK", "BOTTOM", "RIGHT", "FRONT", "TOP", "LEFT", "FRONT"], "required_slots": ["LEFT", "BACK", "BOTTOM", "RIGHT", "FRONT", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "N", "rotation": 180}, "BOTTOM": {"patternId": "U", "rotation": 180}, "FRONT": {"patternId": "D", "rotation": 90}, "BACK": {"patternId": "smile", "rotation": 180}, "LEFT": {"patternId": "F", "rotation": 0}, "RIGHT": {"patternId": "A", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "N", "rotation": 180}, "BOTTOM": {"patternId": "U", "rotation": 180}, "FRONT": {"patternId": "D", "rotation": 90}, "BACK": {"patternId": "smile", "rotation": 180}, "LEFT": {"patternId": "F", "rotation": 0}, "RIGHT": {"patternId": "A", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C339\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> E -> N -> E -> N -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=F, rotation=180, flipVertical=true\n- step 2: patternId=smile, rotation=270, flipVertical=true\n- step 3: patternId=U, rotation=270, flipVertical=true\n- step 4: patternId=A, rotation=180, flipVertical=true\n- step 5: patternId=D, rotation=270, flipVertical=true\n- step 6: patternId=N, rotation=0, flipVertical=true\n- step 7: patternId=F, rotation=180, flipVertical=true\n- step 8: patternId=D, rotation=0, flipVertical=true\n- allowed patternId values for this task: F, smile, U, A, D, N, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C339"} +{"sample_id": "C340", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> W -> N -> W -> N -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "W", "N", "W", "N", "E", "E"], "observed_path_faces": [{"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C340_path_sequence.png"}, "metadata": {"level_id": 340, "name": "Reconstruct 340", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-340.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["U", "star", "V", "arrow_right", "F", "A"], "start_x": 1, "start_y": 3, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "U", "rotation": 180}, "BOTTOM": {"patternId": "A", "rotation": 180}, "FRONT": {"patternId": "star", "rotation": 90}, "BACK": {"patternId": "arrow_right", "rotation": 0}, "LEFT": {"patternId": "F", "rotation": 0}, "RIGHT": {"patternId": "V", "rotation": 270}}, "bottom_faces": [{"patternId": "A", "rotation": 180, "x": 1, "y": 3}, {"patternId": "V", "rotation": 0, "x": 2, "y": 3}, {"patternId": "U", "rotation": 0, "x": 3, "y": 3}, {"patternId": "V", "rotation": 0, "x": 2, "y": 3}, {"patternId": "arrow_right", "rotation": 90, "x": 2, "y": 2}, {"patternId": "A", "rotation": 90, "x": 1, "y": 2}, {"patternId": "F", "rotation": 180, "x": 1, "y": 1}, {"patternId": "arrow_right", "rotation": 180, "x": 2, "y": 1}, {"patternId": "V", "rotation": 90, "x": 3, "y": 1}], "slot_sequence": ["RIGHT", "TOP", "RIGHT", "BACK", "BOTTOM", "LEFT", "BACK", "RIGHT"], "required_slots": ["RIGHT", "TOP", "BACK", "BOTTOM", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "U", "rotation": 180}, "BOTTOM": {"patternId": "A", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_right", "rotation": 180}, "LEFT": {"patternId": "F", "rotation": 90}, "RIGHT": {"patternId": "V", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "U", "rotation": 180}, "BOTTOM": {"patternId": "A", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_right", "rotation": 180}, "LEFT": {"patternId": "F", "rotation": 90}, "RIGHT": {"patternId": "V", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C340\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> W -> N -> W -> N -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=V, rotation=0, flipVertical=true\n- step 2: patternId=U, rotation=0, flipVertical=true\n- step 3: patternId=V, rotation=0, flipVertical=true\n- step 4: patternId=arrow_right, rotation=90, flipVertical=true\n- step 5: patternId=A, rotation=90, flipVertical=true\n- step 6: patternId=F, rotation=180, flipVertical=true\n- step 7: patternId=arrow_right, rotation=180, flipVertical=true\n- step 8: patternId=V, rotation=90, flipVertical=true\n- allowed patternId values for this task: V, U, arrow_right, A, F, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C340"} +{"sample_id": "C341", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> W -> N -> W -> S -> W -> W -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "W", "N", "W", "S", "W", "W", "W", "S"], "observed_path_faces": [{"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C341_path_sequence.png"}, "metadata": {"level_id": 341, "name": "Reconstruct 341", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-341.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["6", "2", "B", "4", "smile", "D"], "start_x": 5, "start_y": 2, "grid_width": 8, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "6", "rotation": 270}, "BOTTOM": {"patternId": "D", "rotation": 90}, "FRONT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "4", "rotation": 90}, "LEFT": {"patternId": "smile", "rotation": 90}, "RIGHT": {"patternId": "B", "rotation": 270}}, "bottom_faces": [{"patternId": "D", "rotation": 90, "x": 5, "y": 2}, {"patternId": "B", "rotation": 0, "x": 6, "y": 2}, {"patternId": "D", "rotation": 90, "x": 5, "y": 2}, {"patternId": "4", "rotation": 270, "x": 5, "y": 1}, {"patternId": "smile", "rotation": 270, "x": 4, "y": 1}, {"patternId": "D", "rotation": 0, "x": 4, "y": 2}, {"patternId": "2", "rotation": 180, "x": 3, "y": 2}, {"patternId": "6", "rotation": 180, "x": 2, "y": 2}, {"patternId": "4", "rotation": 180, "x": 1, "y": 2}, {"patternId": "B", "rotation": 0, "x": 1, "y": 3}], "slot_sequence": ["RIGHT", "BOTTOM", "BACK", "LEFT", "BOTTOM", "FRONT", "TOP", "BACK", "RIGHT"], "required_slots": ["RIGHT", "BOTTOM", "BACK", "LEFT", "FRONT", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "6", "rotation": 270}, "BOTTOM": {"patternId": "D", "rotation": 90}, "FRONT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "4", "rotation": 270}, "LEFT": {"patternId": "smile", "rotation": 180}, "RIGHT": {"patternId": "B", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 270}, "BOTTOM": {"patternId": "D", "rotation": 90}, "FRONT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "4", "rotation": 270}, "LEFT": {"patternId": "smile", "rotation": 180}, "RIGHT": {"patternId": "B", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C341\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): E -> W -> N -> W -> S -> W -> W -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=B, rotation=0, flipVertical=true\n- step 2: patternId=D, rotation=90, flipVertical=true\n- step 3: patternId=4, rotation=270, flipVertical=true\n- step 4: patternId=smile, rotation=270, flipVertical=true\n- step 5: patternId=D, rotation=0, flipVertical=true\n- step 6: patternId=2, rotation=180, flipVertical=true\n- step 7: patternId=6, rotation=180, flipVertical=true\n- step 8: patternId=4, rotation=180, flipVertical=true\n- step 9: patternId=B, rotation=0, flipVertical=true\n- allowed patternId values for this task: B, D, 4, smile, 2, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C341"} +{"sample_id": "C342", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> E -> E -> N -> N -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "E", "E", "N", "N", "S", "S"], "observed_path_faces": [{"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C342_path_sequence.png"}, "metadata": {"level_id": 342, "name": "Reconstruct 342", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-342.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["circle", "1", "1", "B", "O", "square"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "circle", "rotation": 90}, "BOTTOM": {"patternId": "square", "rotation": 180}, "FRONT": {"patternId": "1", "rotation": 180}, "BACK": {"patternId": "B", "rotation": 270}, "LEFT": {"patternId": "O", "rotation": 90}, "RIGHT": {"patternId": "1", "rotation": 270}}, "bottom_faces": [{"patternId": "square", "rotation": 180, "x": 1, "y": 1}, {"patternId": "1", "rotation": 180, "x": 1, "y": 2}, {"patternId": "circle", "rotation": 90, "x": 1, "y": 3}, {"patternId": "1", "rotation": 180, "x": 2, "y": 3}, {"patternId": "square", "rotation": 0, "x": 3, "y": 3}, {"patternId": "1", "rotation": 0, "x": 3, "y": 2}, {"patternId": "circle", "rotation": 270, "x": 3, "y": 1}, {"patternId": "1", "rotation": 0, "x": 3, "y": 2}, {"patternId": "square", "rotation": 0, "x": 3, "y": 3}], "slot_sequence": ["FRONT", "TOP", "RIGHT", "BOTTOM", "FRONT", "TOP", "FRONT", "BOTTOM"], "required_slots": ["FRONT", "TOP", "RIGHT", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "circle", "rotation": 90}, "BOTTOM": {"patternId": "square", "rotation": 180}, "FRONT": {"patternId": "1", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 90}, "BOTTOM": {"patternId": "square", "rotation": 180}, "FRONT": {"patternId": "1", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C342\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> E -> E -> N -> N -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=1, rotation=180, flipVertical=true\n- step 2: patternId=circle, rotation=90, flipVertical=true\n- step 3: patternId=1, rotation=180, flipVertical=true\n- step 4: patternId=square, rotation=0, flipVertical=true\n- step 5: patternId=1, rotation=0, flipVertical=true\n- step 6: patternId=circle, rotation=270, flipVertical=true\n- step 7: patternId=1, rotation=0, flipVertical=true\n- step 8: patternId=square, rotation=0, flipVertical=true\n- allowed patternId values for this task: 1, circle, square, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C342"} +{"sample_id": "C343", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> S -> S -> W -> S -> W -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "S", "S", "W", "S", "W", "W", "N"], "observed_path_faces": [{"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C343_path_sequence.png"}, "metadata": {"level_id": 343, "name": "Reconstruct 343", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-343.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["6", "6", "F", "J", "L", "J"], "start_x": 5, "start_y": 2, "grid_width": 7, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "6", "rotation": 180}, "BOTTOM": {"patternId": "J", "rotation": 0}, "FRONT": {"patternId": "6", "rotation": 90}, "BACK": {"patternId": "J", "rotation": 180}, "LEFT": {"patternId": "L", "rotation": 0}, "RIGHT": {"patternId": "F", "rotation": 270}}, "bottom_faces": [{"patternId": "J", "rotation": 0, "x": 5, "y": 2}, {"patternId": "J", "rotation": 0, "x": 5, "y": 1}, {"patternId": "L", "rotation": 180, "x": 4, "y": 1}, {"patternId": "J", "rotation": 270, "x": 4, "y": 2}, {"patternId": "F", "rotation": 270, "x": 4, "y": 3}, {"patternId": "6", "rotation": 90, "x": 3, "y": 3}, {"patternId": "6", "rotation": 180, "x": 3, "y": 4}, {"patternId": "L", "rotation": 90, "x": 2, "y": 4}, {"patternId": "J", "rotation": 180, "x": 1, "y": 4}, {"patternId": "6", "rotation": 270, "x": 1, "y": 3}], "slot_sequence": ["BACK", "LEFT", "BOTTOM", "RIGHT", "FRONT", "TOP", "LEFT", "BOTTOM", "FRONT"], "required_slots": ["BACK", "LEFT", "BOTTOM", "RIGHT", "FRONT", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "6", "rotation": 180}, "BOTTOM": {"patternId": "J", "rotation": 0}, "FRONT": {"patternId": "6", "rotation": 90}, "BACK": {"patternId": "J", "rotation": 0}, "LEFT": {"patternId": "L", "rotation": 90}, "RIGHT": {"patternId": "F", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 180}, "BOTTOM": {"patternId": "J", "rotation": 0}, "FRONT": {"patternId": "6", "rotation": 90}, "BACK": {"patternId": "J", "rotation": 0}, "LEFT": {"patternId": "L", "rotation": 90}, "RIGHT": {"patternId": "F", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C343\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> S -> S -> W -> S -> W -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=J, rotation=0, flipVertical=true\n- step 2: patternId=L, rotation=180, flipVertical=true\n- step 3: patternId=J, rotation=270, flipVertical=true\n- step 4: patternId=F, rotation=270, flipVertical=true\n- step 5: patternId=6, rotation=90, flipVertical=true\n- step 6: patternId=6, rotation=180, flipVertical=true\n- step 7: patternId=L, rotation=90, flipVertical=true\n- step 8: patternId=J, rotation=180, flipVertical=true\n- step 9: patternId=6, rotation=270, flipVertical=true\n- allowed patternId values for this task: J, L, F, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C343"} +{"sample_id": "C344", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> E -> E -> S -> E -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "E", "E", "S", "E", "N", "W"], "observed_path_faces": [{"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C344_path_sequence.png"}, "metadata": {"level_id": 344, "name": "Reconstruct 344", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-344.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["diamond", "9", "arrow_left", "arrow_down", "plus", "P"], "start_x": 1, "start_y": 3, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "diamond", "rotation": 0}, "BOTTOM": {"patternId": "P", "rotation": 90}, "FRONT": {"patternId": "9", "rotation": 270}, "BACK": {"patternId": "arrow_down", "rotation": 270}, "LEFT": {"patternId": "plus", "rotation": 90}, "RIGHT": {"patternId": "arrow_left", "rotation": 0}}, "bottom_faces": [{"patternId": "P", "rotation": 90, "x": 1, "y": 3}, {"patternId": "arrow_down", "rotation": 90, "x": 1, "y": 2}, {"patternId": "diamond", "rotation": 0, "x": 1, "y": 1}, {"patternId": "arrow_left", "rotation": 270, "x": 2, "y": 1}, {"patternId": "P", "rotation": 270, "x": 3, "y": 1}, {"patternId": "arrow_down", "rotation": 270, "x": 3, "y": 2}, {"patternId": "plus", "rotation": 90, "x": 4, "y": 2}, {"patternId": "P", "rotation": 180, "x": 4, "y": 1}, {"patternId": "arrow_down", "rotation": 180, "x": 3, "y": 1}], "slot_sequence": ["BACK", "TOP", "RIGHT", "BOTTOM", "BACK", "LEFT", "BOTTOM", "BACK"], "required_slots": ["BACK", "TOP", "RIGHT", "BOTTOM", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "diamond", "rotation": 0}, "BOTTOM": {"patternId": "P", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_down", "rotation": 90}, "LEFT": {"patternId": "plus", "rotation": 180}, "RIGHT": {"patternId": "arrow_left", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "diamond", "rotation": 0}, "BOTTOM": {"patternId": "P", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_down", "rotation": 90}, "LEFT": {"patternId": "plus", "rotation": 180}, "RIGHT": {"patternId": "arrow_left", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C344\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> E -> E -> S -> E -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_down, rotation=90, flipVertical=true\n- step 2: patternId=diamond, rotation=0, flipVertical=true\n- step 3: patternId=arrow_left, rotation=270, flipVertical=true\n- step 4: patternId=P, rotation=270, flipVertical=true\n- step 5: patternId=arrow_down, rotation=270, flipVertical=true\n- step 6: patternId=plus, rotation=90, flipVertical=true\n- step 7: patternId=P, rotation=180, flipVertical=true\n- step 8: patternId=arrow_down, rotation=180, flipVertical=true\n- allowed patternId values for this task: arrow_down, diamond, arrow_left, P, plus, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C344"} +{"sample_id": "C345", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> N -> W -> S -> E -> N -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "N", "W", "S", "E", "N", "N", "E"], "observed_path_faces": [{"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C345_path_sequence.png"}, "metadata": {"level_id": 345, "name": "Reconstruct 345", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-345.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["E", "heart", "arrow_left", "4", "heart", "circle"], "start_x": 4, "start_y": 3, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "E", "rotation": 270}, "BOTTOM": {"patternId": "circle", "rotation": 180}, "FRONT": {"patternId": "heart", "rotation": 0}, "BACK": {"patternId": "4", "rotation": 270}, "LEFT": {"patternId": "heart", "rotation": 270}, "RIGHT": {"patternId": "arrow_left", "rotation": 0}}, "bottom_faces": [{"patternId": "circle", "rotation": 180, "x": 4, "y": 3}, {"patternId": "heart", "rotation": 180, "x": 3, "y": 3}, {"patternId": "E", "rotation": 90, "x": 2, "y": 3}, {"patternId": "4", "rotation": 270, "x": 2, "y": 2}, {"patternId": "arrow_left", "rotation": 0, "x": 1, "y": 2}, {"patternId": "E", "rotation": 0, "x": 1, "y": 3}, {"patternId": "4", "rotation": 180, "x": 2, "y": 3}, {"patternId": "arrow_left", "rotation": 270, "x": 2, "y": 2}, {"patternId": "heart", "rotation": 270, "x": 2, "y": 1}, {"patternId": "circle", "rotation": 90, "x": 3, "y": 1}], "slot_sequence": ["LEFT", "TOP", "BACK", "RIGHT", "TOP", "BACK", "RIGHT", "FRONT", "BOTTOM"], "required_slots": ["LEFT", "TOP", "BACK", "RIGHT", "FRONT", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "E", "rotation": 270}, "BOTTOM": {"patternId": "circle", "rotation": 180}, "FRONT": {"patternId": "heart", "rotation": 0}, "BACK": {"patternId": "4", "rotation": 90}, "LEFT": {"patternId": "heart", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "E", "rotation": 270}, "BOTTOM": {"patternId": "circle", "rotation": 180}, "FRONT": {"patternId": "heart", "rotation": 0}, "BACK": {"patternId": "4", "rotation": 90}, "LEFT": {"patternId": "heart", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C345\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> N -> W -> S -> E -> N -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=heart, rotation=180, flipVertical=true\n- step 2: patternId=E, rotation=90, flipVertical=true\n- step 3: patternId=4, rotation=270, flipVertical=true\n- step 4: patternId=arrow_left, rotation=0, flipVertical=true\n- step 5: patternId=E, rotation=0, flipVertical=true\n- step 6: patternId=4, rotation=180, flipVertical=true\n- step 7: patternId=arrow_left, rotation=270, flipVertical=true\n- step 8: patternId=heart, rotation=270, flipVertical=true\n- step 9: patternId=circle, rotation=90, flipVertical=true\n- allowed patternId values for this task: heart, E, 4, arrow_left, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C345"} +{"sample_id": "C346", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> N -> N -> N -> W -> N -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "N", "N", "N", "W", "N", "E", "E"], "observed_path_faces": [{"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C346_path_sequence.png"}, "metadata": {"level_id": 346, "name": "Reconstruct 346", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-346.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["B", "diamond", "G", "3", "4", "F"], "start_x": 2, "start_y": 3, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "B", "rotation": 270}, "BOTTOM": {"patternId": "F", "rotation": 90}, "FRONT": {"patternId": "diamond", "rotation": 270}, "BACK": {"patternId": "3", "rotation": 90}, "LEFT": {"patternId": "4", "rotation": 270}, "RIGHT": {"patternId": "G", "rotation": 180}}, "bottom_faces": [{"patternId": "F", "rotation": 90, "x": 2, "y": 3}, {"patternId": "diamond", "rotation": 270, "x": 2, "y": 4}, {"patternId": "B", "rotation": 270, "x": 2, "y": 5}, {"patternId": "diamond", "rotation": 270, "x": 2, "y": 4}, {"patternId": "F", "rotation": 90, "x": 2, "y": 3}, {"patternId": "3", "rotation": 270, "x": 2, "y": 2}, {"patternId": "4", "rotation": 90, "x": 1, "y": 2}, {"patternId": "B", "rotation": 0, "x": 1, "y": 1}, {"patternId": "3", "rotation": 0, "x": 2, "y": 1}, {"patternId": "F", "rotation": 180, "x": 3, "y": 1}], "slot_sequence": ["FRONT", "TOP", "FRONT", "BOTTOM", "BACK", "LEFT", "TOP", "BACK", "BOTTOM"], "required_slots": ["FRONT", "TOP", "BOTTOM", "BACK", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "B", "rotation": 270}, "BOTTOM": {"patternId": "F", "rotation": 90}, "FRONT": {"patternId": "diamond", "rotation": 270}, "BACK": {"patternId": "3", "rotation": 270}, "LEFT": {"patternId": "4", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "B", "rotation": 270}, "BOTTOM": {"patternId": "F", "rotation": 90}, "FRONT": {"patternId": "diamond", "rotation": 270}, "BACK": {"patternId": "3", "rotation": 270}, "LEFT": {"patternId": "4", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C346\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> N -> N -> N -> W -> N -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=diamond, rotation=270, flipVertical=true\n- step 2: patternId=B, rotation=270, flipVertical=true\n- step 3: patternId=diamond, rotation=270, flipVertical=true\n- step 4: patternId=F, rotation=90, flipVertical=true\n- step 5: patternId=3, rotation=270, flipVertical=true\n- step 6: patternId=4, rotation=90, flipVertical=true\n- step 7: patternId=B, rotation=0, flipVertical=true\n- step 8: patternId=3, rotation=0, flipVertical=true\n- step 9: patternId=F, rotation=180, flipVertical=true\n- allowed patternId values for this task: diamond, B, F, 3, 4, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C346"} +{"sample_id": "C347", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> E -> S -> W -> N -> S -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "E", "S", "W", "N", "S", "E", "S"], "observed_path_faces": [{"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C347_path_sequence.png"}, "metadata": {"level_id": 347, "name": "Reconstruct 347", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-347.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["S", "E", "2", "T", "G", "arrow_right"], "start_x": 1, "start_y": 2, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "S", "rotation": 90}, "BOTTOM": {"patternId": "arrow_right", "rotation": 180}, "FRONT": {"patternId": "E", "rotation": 90}, "BACK": {"patternId": "T", "rotation": 0}, "LEFT": {"patternId": "G", "rotation": 90}, "RIGHT": {"patternId": "2", "rotation": 270}}, "bottom_faces": [{"patternId": "arrow_right", "rotation": 180, "x": 1, "y": 2}, {"patternId": "2", "rotation": 0, "x": 2, "y": 2}, {"patternId": "T", "rotation": 90, "x": 2, "y": 1}, {"patternId": "S", "rotation": 0, "x": 3, "y": 1}, {"patternId": "2", "rotation": 90, "x": 3, "y": 2}, {"patternId": "T", "rotation": 180, "x": 2, "y": 2}, {"patternId": "S", "rotation": 90, "x": 2, "y": 1}, {"patternId": "T", "rotation": 180, "x": 2, "y": 2}, {"patternId": "2", "rotation": 90, "x": 3, "y": 2}, {"patternId": "arrow_right", "rotation": 270, "x": 3, "y": 3}], "slot_sequence": ["RIGHT", "BACK", "TOP", "RIGHT", "BACK", "TOP", "BACK", "RIGHT", "BOTTOM"], "required_slots": ["RIGHT", "BACK", "TOP", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "S", "rotation": 90}, "BOTTOM": {"patternId": "arrow_right", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "2", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 90}, "BOTTOM": {"patternId": "arrow_right", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "2", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C347\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> E -> S -> W -> N -> S -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=2, rotation=0, flipVertical=true\n- step 2: patternId=T, rotation=90, flipVertical=true\n- step 3: patternId=S, rotation=0, flipVertical=true\n- step 4: patternId=2, rotation=90, flipVertical=true\n- step 5: patternId=T, rotation=180, flipVertical=true\n- step 6: patternId=S, rotation=90, flipVertical=true\n- step 7: patternId=T, rotation=180, flipVertical=true\n- step 8: patternId=2, rotation=90, flipVertical=true\n- step 9: patternId=arrow_right, rotation=270, flipVertical=true\n- allowed patternId values for this task: 2, T, S, arrow_right, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C347"} +{"sample_id": "C348", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> E -> S -> S -> S -> E -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "E", "S", "S", "S", "E", "W"], "observed_path_faces": [{"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C348_path_sequence.png"}, "metadata": {"level_id": 348, "name": "Reconstruct 348", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-348.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["7", "2", "3", "W", "P", "W"], "start_x": 1, "start_y": 2, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "7", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 180}, "FRONT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "W", "rotation": 180}, "LEFT": {"patternId": "P", "rotation": 270}, "RIGHT": {"patternId": "3", "rotation": 0}}, "bottom_faces": [{"patternId": "W", "rotation": 180, "x": 1, "y": 2}, {"patternId": "W", "rotation": 0, "x": 1, "y": 1}, {"patternId": "3", "rotation": 180, "x": 2, "y": 1}, {"patternId": "2", "rotation": 90, "x": 3, "y": 1}, {"patternId": "W", "rotation": 0, "x": 3, "y": 2}, {"patternId": "W", "rotation": 180, "x": 3, "y": 3}, {"patternId": "7", "rotation": 180, "x": 3, "y": 4}, {"patternId": "P", "rotation": 180, "x": 4, "y": 4}, {"patternId": "7", "rotation": 180, "x": 3, "y": 4}], "slot_sequence": ["BACK", "RIGHT", "FRONT", "BOTTOM", "BACK", "TOP", "LEFT", "TOP"], "required_slots": ["BACK", "RIGHT", "FRONT", "BOTTOM", "TOP", "LEFT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "7", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 180}, "FRONT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "W", "rotation": 0}, "LEFT": {"patternId": "P", "rotation": 0}, "RIGHT": {"patternId": "3", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "7", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 180}, "FRONT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "W", "rotation": 0}, "LEFT": {"patternId": "P", "rotation": 0}, "RIGHT": {"patternId": "3", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C348\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> E -> S -> S -> S -> E -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=W, rotation=0, flipVertical=true\n- step 2: patternId=3, rotation=180, flipVertical=true\n- step 3: patternId=2, rotation=90, flipVertical=true\n- step 4: patternId=W, rotation=0, flipVertical=true\n- step 5: patternId=W, rotation=180, flipVertical=true\n- step 6: patternId=7, rotation=180, flipVertical=true\n- step 7: patternId=P, rotation=180, flipVertical=true\n- step 8: patternId=7, rotation=180, flipVertical=true\n- allowed patternId values for this task: W, 3, 2, 7, P, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C348"} +{"sample_id": "C349", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> N -> W -> E -> N -> W -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "N", "W", "E", "N", "W", "N", "W"], "observed_path_faces": [{"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C349_path_sequence.png"}, "metadata": {"level_id": 349, "name": "Reconstruct 349", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-349.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["plus", "G", "Q", "arrow_up", "G", "arrow_up"], "start_x": 4, "start_y": 3, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "plus", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 180}, "FRONT": {"patternId": "G", "rotation": 180}, "BACK": {"patternId": "arrow_up", "rotation": 180}, "LEFT": {"patternId": "G", "rotation": 0}, "RIGHT": {"patternId": "Q", "rotation": 270}}, "bottom_faces": [{"patternId": "arrow_up", "rotation": 180, "x": 4, "y": 3}, {"patternId": "G", "rotation": 180, "x": 4, "y": 4}, {"patternId": "G", "rotation": 0, "x": 3, "y": 4}, {"patternId": "arrow_up", "rotation": 270, "x": 3, "y": 3}, {"patternId": "arrow_up", "rotation": 90, "x": 2, "y": 3}, {"patternId": "arrow_up", "rotation": 270, "x": 3, "y": 3}, {"patternId": "Q", "rotation": 90, "x": 3, "y": 2}, {"patternId": "arrow_up", "rotation": 0, "x": 2, "y": 2}, {"patternId": "plus", "rotation": 0, "x": 2, "y": 1}, {"patternId": "G", "rotation": 90, "x": 1, "y": 1}], "slot_sequence": ["FRONT", "LEFT", "BOTTOM", "BACK", "BOTTOM", "RIGHT", "BACK", "TOP", "LEFT"], "required_slots": ["FRONT", "LEFT", "BOTTOM", "BACK", "RIGHT", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "plus", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 180}, "FRONT": {"patternId": "G", "rotation": 180}, "BACK": {"patternId": "arrow_up", "rotation": 0}, "LEFT": {"patternId": "G", "rotation": 90}, "RIGHT": {"patternId": "Q", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "plus", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 180}, "FRONT": {"patternId": "G", "rotation": 180}, "BACK": {"patternId": "arrow_up", "rotation": 0}, "LEFT": {"patternId": "G", "rotation": 90}, "RIGHT": {"patternId": "Q", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C349\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> N -> W -> E -> N -> W -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=G, rotation=180, flipVertical=true\n- step 2: patternId=G, rotation=0, flipVertical=true\n- step 3: patternId=arrow_up, rotation=270, flipVertical=true\n- step 4: patternId=arrow_up, rotation=90, flipVertical=true\n- step 5: patternId=arrow_up, rotation=270, flipVertical=true\n- step 6: patternId=Q, rotation=90, flipVertical=true\n- step 7: patternId=arrow_up, rotation=0, flipVertical=true\n- step 8: patternId=plus, rotation=0, flipVertical=true\n- step 9: patternId=G, rotation=90, flipVertical=true\n- allowed patternId values for this task: G, arrow_up, Q, plus, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C349"} +{"sample_id": "C350", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> S -> S -> W -> S -> S -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "S", "S", "W", "S", "S", "W", "W"], "observed_path_faces": [{"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C350_path_sequence.png"}, "metadata": {"level_id": 350, "name": "Reconstruct 350", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-350.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["R", "N", "P", "H", "V", "arrow_up"], "start_x": 3, "start_y": 1, "grid_width": 6, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "R", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "N", "rotation": 90}, "BACK": {"patternId": "H", "rotation": 180}, "LEFT": {"patternId": "V", "rotation": 0}, "RIGHT": {"patternId": "P", "rotation": 90}}, "bottom_faces": [{"patternId": "arrow_up", "rotation": 270, "x": 3, "y": 1}, {"patternId": "N", "rotation": 90, "x": 3, "y": 2}, {"patternId": "P", "rotation": 90, "x": 4, "y": 2}, {"patternId": "R", "rotation": 90, "x": 4, "y": 3}, {"patternId": "V", "rotation": 180, "x": 4, "y": 4}, {"patternId": "N", "rotation": 270, "x": 3, "y": 4}, {"patternId": "arrow_up", "rotation": 90, "x": 3, "y": 5}, {"patternId": "H", "rotation": 180, "x": 3, "y": 6}, {"patternId": "P", "rotation": 90, "x": 2, "y": 6}, {"patternId": "N", "rotation": 90, "x": 1, "y": 6}], "slot_sequence": ["FRONT", "RIGHT", "TOP", "LEFT", "FRONT", "BOTTOM", "BACK", "RIGHT", "FRONT"], "required_slots": ["FRONT", "RIGHT", "TOP", "LEFT", "BOTTOM", "BACK"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "R", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "N", "rotation": 90}, "BACK": {"patternId": "H", "rotation": 0}, "LEFT": {"patternId": "V", "rotation": 90}, "RIGHT": {"patternId": "P", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "R", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "N", "rotation": 90}, "BACK": {"patternId": "H", "rotation": 0}, "LEFT": {"patternId": "V", "rotation": 90}, "RIGHT": {"patternId": "P", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C350\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> S -> S -> W -> S -> S -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=N, rotation=90, flipVertical=true\n- step 2: patternId=P, rotation=90, flipVertical=true\n- step 3: patternId=R, rotation=90, flipVertical=true\n- step 4: patternId=V, rotation=180, flipVertical=true\n- step 5: patternId=N, rotation=270, flipVertical=true\n- step 6: patternId=arrow_up, rotation=90, flipVertical=true\n- step 7: patternId=H, rotation=180, flipVertical=true\n- step 8: patternId=P, rotation=90, flipVertical=true\n- step 9: patternId=N, rotation=90, flipVertical=true\n- allowed patternId values for this task: N, P, R, V, arrow_up, H, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C350"} +{"sample_id": "C351", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> E -> N -> W -> N -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "E", "N", "W", "N", "E", "E"], "observed_path_faces": [{"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C351_path_sequence.png"}, "metadata": {"level_id": 351, "name": "Reconstruct 351", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-351.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["smile", "F", "7", "F", "heart", "E"], "start_x": 1, "start_y": 2, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "smile", "rotation": 180}, "BOTTOM": {"patternId": "E", "rotation": 180}, "FRONT": {"patternId": "F", "rotation": 90}, "BACK": {"patternId": "F", "rotation": 180}, "LEFT": {"patternId": "heart", "rotation": 90}, "RIGHT": {"patternId": "7", "rotation": 90}}, "bottom_faces": [{"patternId": "E", "rotation": 180, "x": 1, "y": 2}, {"patternId": "7", "rotation": 180, "x": 2, "y": 2}, {"patternId": "F", "rotation": 180, "x": 2, "y": 3}, {"patternId": "smile", "rotation": 270, "x": 3, "y": 3}, {"patternId": "7", "rotation": 90, "x": 3, "y": 2}, {"patternId": "F", "rotation": 90, "x": 2, "y": 2}, {"patternId": "E", "rotation": 180, "x": 2, "y": 1}, {"patternId": "7", "rotation": 180, "x": 3, "y": 1}, {"patternId": "smile", "rotation": 0, "x": 4, "y": 1}], "slot_sequence": ["RIGHT", "FRONT", "TOP", "RIGHT", "FRONT", "BOTTOM", "RIGHT", "TOP"], "required_slots": ["RIGHT", "FRONT", "TOP", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "smile", "rotation": 180}, "BOTTOM": {"patternId": "E", "rotation": 180}, "FRONT": {"patternId": "F", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "7", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 180}, "BOTTOM": {"patternId": "E", "rotation": 180}, "FRONT": {"patternId": "F", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "7", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C351\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> E -> N -> W -> N -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=7, rotation=180, flipVertical=true\n- step 2: patternId=F, rotation=180, flipVertical=true\n- step 3: patternId=smile, rotation=270, flipVertical=true\n- step 4: patternId=7, rotation=90, flipVertical=true\n- step 5: patternId=F, rotation=90, flipVertical=true\n- step 6: patternId=E, rotation=180, flipVertical=true\n- step 7: patternId=7, rotation=180, flipVertical=true\n- step 8: patternId=smile, rotation=0, flipVertical=true\n- allowed patternId values for this task: 7, F, smile, E, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C351"} +{"sample_id": "C352", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> W -> N -> E -> E -> S -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "W", "N", "E", "E", "S", "E", "E"], "observed_path_faces": [{"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C352_path_sequence.png"}, "metadata": {"level_id": 352, "name": "Reconstruct 352", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-352.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["S", "V", "K", "U", "7", "N"], "start_x": 3, "start_y": 1, "grid_width": 7, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "S", "rotation": 180}, "BOTTOM": {"patternId": "N", "rotation": 180}, "FRONT": {"patternId": "V", "rotation": 180}, "BACK": {"patternId": "U", "rotation": 90}, "LEFT": {"patternId": "7", "rotation": 0}, "RIGHT": {"patternId": "K", "rotation": 90}}, "bottom_faces": [{"patternId": "N", "rotation": 180, "x": 3, "y": 1}, {"patternId": "7", "rotation": 270, "x": 2, "y": 1}, {"patternId": "V", "rotation": 90, "x": 2, "y": 2}, {"patternId": "S", "rotation": 90, "x": 1, "y": 2}, {"patternId": "7", "rotation": 0, "x": 1, "y": 1}, {"patternId": "V", "rotation": 180, "x": 2, "y": 1}, {"patternId": "K", "rotation": 90, "x": 3, "y": 1}, {"patternId": "S", "rotation": 270, "x": 3, "y": 2}, {"patternId": "U", "rotation": 0, "x": 4, "y": 2}, {"patternId": "N", "rotation": 270, "x": 5, "y": 2}], "slot_sequence": ["LEFT", "FRONT", "TOP", "LEFT", "FRONT", "RIGHT", "TOP", "BACK", "BOTTOM"], "required_slots": ["LEFT", "FRONT", "TOP", "RIGHT", "BACK", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "S", "rotation": 180}, "BOTTOM": {"patternId": "N", "rotation": 180}, "FRONT": {"patternId": "V", "rotation": 180}, "BACK": {"patternId": "U", "rotation": 270}, "LEFT": {"patternId": "7", "rotation": 90}, "RIGHT": {"patternId": "K", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 180}, "BOTTOM": {"patternId": "N", "rotation": 180}, "FRONT": {"patternId": "V", "rotation": 180}, "BACK": {"patternId": "U", "rotation": 270}, "LEFT": {"patternId": "7", "rotation": 90}, "RIGHT": {"patternId": "K", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C352\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> W -> N -> E -> E -> S -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=7, rotation=270, flipVertical=true\n- step 2: patternId=V, rotation=90, flipVertical=true\n- step 3: patternId=S, rotation=90, flipVertical=true\n- step 4: patternId=7, rotation=0, flipVertical=true\n- step 5: patternId=V, rotation=180, flipVertical=true\n- step 6: patternId=K, rotation=90, flipVertical=true\n- step 7: patternId=S, rotation=270, flipVertical=true\n- step 8: patternId=U, rotation=0, flipVertical=true\n- step 9: patternId=N, rotation=270, flipVertical=true\n- allowed patternId values for this task: 7, V, S, K, U, N, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C352"} +{"sample_id": "C353", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> W -> E -> W -> S -> E -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "W", "E", "W", "S", "E", "S", "E"], "observed_path_faces": [{"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C353_path_sequence.png"}, "metadata": {"level_id": 353, "name": "Reconstruct 353", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-353.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["G", "C", "J", "square", "T", "G"], "start_x": 2, "start_y": 1, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "G", "rotation": 0}, "BOTTOM": {"patternId": "G", "rotation": 0}, "FRONT": {"patternId": "C", "rotation": 90}, "BACK": {"patternId": "square", "rotation": 0}, "LEFT": {"patternId": "T", "rotation": 90}, "RIGHT": {"patternId": "J", "rotation": 180}}, "bottom_faces": [{"patternId": "G", "rotation": 0, "x": 2, "y": 1}, {"patternId": "C", "rotation": 90, "x": 2, "y": 2}, {"patternId": "G", "rotation": 0, "x": 2, "y": 3}, {"patternId": "T", "rotation": 180, "x": 1, "y": 3}, {"patternId": "G", "rotation": 0, "x": 2, "y": 3}, {"patternId": "T", "rotation": 180, "x": 1, "y": 3}, {"patternId": "square", "rotation": 90, "x": 1, "y": 4}, {"patternId": "G", "rotation": 270, "x": 2, "y": 4}, {"patternId": "J", "rotation": 0, "x": 2, "y": 5}, {"patternId": "C", "rotation": 270, "x": 3, "y": 5}], "slot_sequence": ["FRONT", "TOP", "LEFT", "TOP", "LEFT", "BACK", "TOP", "RIGHT", "FRONT"], "required_slots": ["FRONT", "TOP", "LEFT", "BACK", "RIGHT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "G", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "C", "rotation": 90}, "BACK": {"patternId": "square", "rotation": 180}, "LEFT": {"patternId": "T", "rotation": 180}, "RIGHT": {"patternId": "J", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "G", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "C", "rotation": 90}, "BACK": {"patternId": "square", "rotation": 180}, "LEFT": {"patternId": "T", "rotation": 180}, "RIGHT": {"patternId": "J", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C353\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> W -> E -> W -> S -> E -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=C, rotation=90, flipVertical=true\n- step 2: patternId=G, rotation=0, flipVertical=true\n- step 3: patternId=T, rotation=180, flipVertical=true\n- step 4: patternId=G, rotation=0, flipVertical=true\n- step 5: patternId=T, rotation=180, flipVertical=true\n- step 6: patternId=square, rotation=90, flipVertical=true\n- step 7: patternId=G, rotation=270, flipVertical=true\n- step 8: patternId=J, rotation=0, flipVertical=true\n- step 9: patternId=C, rotation=270, flipVertical=true\n- allowed patternId values for this task: C, G, T, square, J, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C353"} +{"sample_id": "C354", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> S -> S -> W -> S -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "S", "S", "W", "S", "W", "N"], "observed_path_faces": [{"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C354_path_sequence.png"}, "metadata": {"level_id": 354, "name": "Reconstruct 354", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-354.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["C", "star", "6", "arrow_down", "P", "A"], "start_x": 2, "start_y": 1, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "C", "rotation": 0}, "BOTTOM": {"patternId": "A", "rotation": 180}, "FRONT": {"patternId": "star", "rotation": 90}, "BACK": {"patternId": "arrow_down", "rotation": 0}, "LEFT": {"patternId": "P", "rotation": 90}, "RIGHT": {"patternId": "6", "rotation": 180}}, "bottom_faces": [{"patternId": "A", "rotation": 180, "x": 2, "y": 1}, {"patternId": "6", "rotation": 270, "x": 3, "y": 1}, {"patternId": "star", "rotation": 180, "x": 3, "y": 2}, {"patternId": "P", "rotation": 180, "x": 3, "y": 3}, {"patternId": "arrow_down", "rotation": 90, "x": 3, "y": 4}, {"patternId": "A", "rotation": 90, "x": 2, "y": 4}, {"patternId": "6", "rotation": 180, "x": 2, "y": 5}, {"patternId": "star", "rotation": 90, "x": 1, "y": 5}, {"patternId": "A", "rotation": 180, "x": 1, "y": 4}], "slot_sequence": ["RIGHT", "FRONT", "LEFT", "BACK", "BOTTOM", "RIGHT", "FRONT", "BOTTOM"], "required_slots": ["RIGHT", "FRONT", "LEFT", "BACK", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "A", "rotation": 180}, "FRONT": {"patternId": "star", "rotation": 90}, "BACK": {"patternId": "arrow_down", "rotation": 180}, "LEFT": {"patternId": "P", "rotation": 180}, "RIGHT": {"patternId": "6", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "A", "rotation": 180}, "FRONT": {"patternId": "star", "rotation": 90}, "BACK": {"patternId": "arrow_down", "rotation": 180}, "LEFT": {"patternId": "P", "rotation": 180}, "RIGHT": {"patternId": "6", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C354\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> S -> S -> W -> S -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=6, rotation=270, flipVertical=true\n- step 2: patternId=star, rotation=180, flipVertical=true\n- step 3: patternId=P, rotation=180, flipVertical=true\n- step 4: patternId=arrow_down, rotation=90, flipVertical=true\n- step 5: patternId=A, rotation=90, flipVertical=true\n- step 6: patternId=6, rotation=180, flipVertical=true\n- step 7: patternId=star, rotation=90, flipVertical=true\n- step 8: patternId=A, rotation=180, flipVertical=true\n- allowed patternId values for this task: 6, star, P, arrow_down, A, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C354"} +{"sample_id": "C355", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> S -> S -> E -> N -> W -> N -> N -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "S", "S", "E", "N", "W", "N", "N", "S"], "observed_path_faces": [{"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C355_path_sequence.png"}, "metadata": {"level_id": 355, "name": "Reconstruct 355", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-355.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["O", "A", "2", "Y", "X", "smile"], "start_x": 1, "start_y": 3, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "O", "rotation": 90}, "BOTTOM": {"patternId": "smile", "rotation": 180}, "FRONT": {"patternId": "A", "rotation": 180}, "BACK": {"patternId": "Y", "rotation": 180}, "LEFT": {"patternId": "X", "rotation": 0}, "RIGHT": {"patternId": "2", "rotation": 90}}, "bottom_faces": [{"patternId": "smile", "rotation": 180, "x": 1, "y": 3}, {"patternId": "Y", "rotation": 0, "x": 1, "y": 2}, {"patternId": "smile", "rotation": 180, "x": 1, "y": 3}, {"patternId": "A", "rotation": 180, "x": 1, "y": 4}, {"patternId": "2", "rotation": 90, "x": 2, "y": 4}, {"patternId": "smile", "rotation": 90, "x": 2, "y": 3}, {"patternId": "A", "rotation": 90, "x": 1, "y": 3}, {"patternId": "X", "rotation": 270, "x": 1, "y": 2}, {"patternId": "Y", "rotation": 90, "x": 1, "y": 1}, {"patternId": "X", "rotation": 270, "x": 1, "y": 2}], "slot_sequence": ["BACK", "BOTTOM", "FRONT", "RIGHT", "BOTTOM", "FRONT", "LEFT", "BACK", "LEFT"], "required_slots": ["BACK", "BOTTOM", "FRONT", "RIGHT", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "smile", "rotation": 180}, "FRONT": {"patternId": "A", "rotation": 180}, "BACK": {"patternId": "Y", "rotation": 0}, "LEFT": {"patternId": "X", "rotation": 90}, "RIGHT": {"patternId": "2", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "smile", "rotation": 180}, "FRONT": {"patternId": "A", "rotation": 180}, "BACK": {"patternId": "Y", "rotation": 0}, "LEFT": {"patternId": "X", "rotation": 90}, "RIGHT": {"patternId": "2", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C355\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): N -> S -> S -> E -> N -> W -> N -> N -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Y, rotation=0, flipVertical=true\n- step 2: patternId=smile, rotation=180, flipVertical=true\n- step 3: patternId=A, rotation=180, flipVertical=true\n- step 4: patternId=2, rotation=90, flipVertical=true\n- step 5: patternId=smile, rotation=90, flipVertical=true\n- step 6: patternId=A, rotation=90, flipVertical=true\n- step 7: patternId=X, rotation=270, flipVertical=true\n- step 8: patternId=Y, rotation=90, flipVertical=true\n- step 9: patternId=X, rotation=270, flipVertical=true\n- allowed patternId values for this task: Y, smile, A, 2, X, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C355"} +{"sample_id": "C356", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> S -> W -> S -> W -> N -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "S", "W", "S", "W", "N", "N", "E"], "observed_path_faces": [{"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C356_path_sequence.png"}, "metadata": {"level_id": 356, "name": "Reconstruct 356", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-356.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Z", "X", "6", "arrow_left", "star", "Z"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "Z", "rotation": 270}, "BOTTOM": {"patternId": "Z", "rotation": 0}, "FRONT": {"patternId": "X", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 90}, "LEFT": {"patternId": "star", "rotation": 90}, "RIGHT": {"patternId": "6", "rotation": 90}}, "bottom_faces": [{"patternId": "Z", "rotation": 0, "x": 3, "y": 1}, {"patternId": "X", "rotation": 0, "x": 3, "y": 2}, {"patternId": "Z", "rotation": 270, "x": 3, "y": 3}, {"patternId": "arrow_left", "rotation": 270, "x": 3, "y": 4}, {"patternId": "star", "rotation": 270, "x": 2, "y": 4}, {"patternId": "Z", "rotation": 270, "x": 2, "y": 5}, {"patternId": "X", "rotation": 270, "x": 1, "y": 5}, {"patternId": "star", "rotation": 0, "x": 1, "y": 4}, {"patternId": "arrow_left", "rotation": 0, "x": 1, "y": 3}, {"patternId": "Z", "rotation": 90, "x": 2, "y": 3}], "slot_sequence": ["FRONT", "TOP", "BACK", "LEFT", "BOTTOM", "FRONT", "LEFT", "BACK", "BOTTOM"], "required_slots": ["FRONT", "TOP", "BACK", "LEFT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "Z", "rotation": 270}, "BOTTOM": {"patternId": "Z", "rotation": 0}, "FRONT": {"patternId": "X", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 270}, "LEFT": {"patternId": "star", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "Z", "rotation": 270}, "BOTTOM": {"patternId": "Z", "rotation": 0}, "FRONT": {"patternId": "X", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 270}, "LEFT": {"patternId": "star", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C356\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> S -> W -> S -> W -> N -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=X, rotation=0, flipVertical=true\n- step 2: patternId=Z, rotation=270, flipVertical=true\n- step 3: patternId=arrow_left, rotation=270, flipVertical=true\n- step 4: patternId=star, rotation=270, flipVertical=true\n- step 5: patternId=Z, rotation=270, flipVertical=true\n- step 6: patternId=X, rotation=270, flipVertical=true\n- step 7: patternId=star, rotation=0, flipVertical=true\n- step 8: patternId=arrow_left, rotation=0, flipVertical=true\n- step 9: patternId=Z, rotation=90, flipVertical=true\n- allowed patternId values for this task: X, Z, arrow_left, star, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C356"} +{"sample_id": "C357", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> E -> N -> W -> N -> E -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "E", "N", "W", "N", "E", "W"], "observed_path_faces": [{"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C357_path_sequence.png"}, "metadata": {"level_id": 357, "name": "Reconstruct 357", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-357.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["3", "D", "W", "7", "G", "Z"], "start_x": 1, "start_y": 2, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "3", "rotation": 180}, "BOTTOM": {"patternId": "Z", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 180}, "BACK": {"patternId": "7", "rotation": 0}, "LEFT": {"patternId": "G", "rotation": 270}, "RIGHT": {"patternId": "W", "rotation": 270}}, "bottom_faces": [{"patternId": "Z", "rotation": 0, "x": 1, "y": 2}, {"patternId": "D", "rotation": 180, "x": 1, "y": 3}, {"patternId": "W", "rotation": 270, "x": 2, "y": 3}, {"patternId": "7", "rotation": 0, "x": 3, "y": 3}, {"patternId": "Z", "rotation": 180, "x": 3, "y": 2}, {"patternId": "W", "rotation": 180, "x": 2, "y": 2}, {"patternId": "D", "rotation": 90, "x": 2, "y": 1}, {"patternId": "Z", "rotation": 270, "x": 3, "y": 1}, {"patternId": "D", "rotation": 90, "x": 2, "y": 1}], "slot_sequence": ["FRONT", "RIGHT", "BACK", "BOTTOM", "RIGHT", "FRONT", "BOTTOM", "FRONT"], "required_slots": ["FRONT", "RIGHT", "BACK", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "Z", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 180}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "W", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "Z", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 180}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "W", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C357\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> E -> N -> W -> N -> E -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=D, rotation=180, flipVertical=true\n- step 2: patternId=W, rotation=270, flipVertical=true\n- step 3: patternId=7, rotation=0, flipVertical=true\n- step 4: patternId=Z, rotation=180, flipVertical=true\n- step 5: patternId=W, rotation=180, flipVertical=true\n- step 6: patternId=D, rotation=90, flipVertical=true\n- step 7: patternId=Z, rotation=270, flipVertical=true\n- step 8: patternId=D, rotation=90, flipVertical=true\n- allowed patternId values for this task: D, W, 7, Z, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C357"} +{"sample_id": "C358", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> E -> N -> E -> S -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "E", "N", "E", "S", "S", "E"], "observed_path_faces": [{"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C358_path_sequence.png"}, "metadata": {"level_id": 358, "name": "Reconstruct 358", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-358.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["B", "V", "5", "M", "Z", "I"], "start_x": 1, "start_y": 3, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "B", "rotation": 90}, "BOTTOM": {"patternId": "I", "rotation": 270}, "FRONT": {"patternId": "V", "rotation": 270}, "BACK": {"patternId": "M", "rotation": 180}, "LEFT": {"patternId": "Z", "rotation": 0}, "RIGHT": {"patternId": "5", "rotation": 180}}, "bottom_faces": [{"patternId": "I", "rotation": 270, "x": 1, "y": 3}, {"patternId": "M", "rotation": 0, "x": 1, "y": 2}, {"patternId": "5", "rotation": 0, "x": 2, "y": 2}, {"patternId": "V", "rotation": 90, "x": 3, "y": 2}, {"patternId": "B", "rotation": 270, "x": 3, "y": 1}, {"patternId": "Z", "rotation": 270, "x": 4, "y": 1}, {"patternId": "V", "rotation": 180, "x": 4, "y": 2}, {"patternId": "5", "rotation": 90, "x": 4, "y": 3}, {"patternId": "I", "rotation": 90, "x": 5, "y": 3}], "slot_sequence": ["BACK", "RIGHT", "FRONT", "TOP", "LEFT", "FRONT", "RIGHT", "BOTTOM"], "required_slots": ["BACK", "RIGHT", "FRONT", "TOP", "LEFT", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "B", "rotation": 90}, "BOTTOM": {"patternId": "I", "rotation": 270}, "FRONT": {"patternId": "V", "rotation": 270}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "Z", "rotation": 90}, "RIGHT": {"patternId": "5", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "B", "rotation": 90}, "BOTTOM": {"patternId": "I", "rotation": 270}, "FRONT": {"patternId": "V", "rotation": 270}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "Z", "rotation": 90}, "RIGHT": {"patternId": "5", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C358\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> E -> N -> E -> S -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=M, rotation=0, flipVertical=true\n- step 2: patternId=5, rotation=0, flipVertical=true\n- step 3: patternId=V, rotation=90, flipVertical=true\n- step 4: patternId=B, rotation=270, flipVertical=true\n- step 5: patternId=Z, rotation=270, flipVertical=true\n- step 6: patternId=V, rotation=180, flipVertical=true\n- step 7: patternId=5, rotation=90, flipVertical=true\n- step 8: patternId=I, rotation=90, flipVertical=true\n- allowed patternId values for this task: M, 5, V, B, Z, I, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C358"} +{"sample_id": "C359", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> W -> N -> W -> S -> W -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "W", "N", "W", "S", "W", "N", "E"], "observed_path_faces": [{"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C359_path_sequence.png"}, "metadata": {"level_id": 359, "name": "Reconstruct 359", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-359.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["heart", "B", "G", "F", "P", "circle"], "start_x": 3, "start_y": 3, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "heart", "rotation": 0}, "BOTTOM": {"patternId": "circle", "rotation": 270}, "FRONT": {"patternId": "B", "rotation": 90}, "BACK": {"patternId": "F", "rotation": 90}, "LEFT": {"patternId": "P", "rotation": 270}, "RIGHT": {"patternId": "G", "rotation": 180}}, "bottom_faces": [{"patternId": "circle", "rotation": 270, "x": 3, "y": 3}, {"patternId": "G", "rotation": 270, "x": 4, "y": 3}, {"patternId": "F", "rotation": 180, "x": 4, "y": 2}, {"patternId": "circle", "rotation": 180, "x": 3, "y": 2}, {"patternId": "P", "rotation": 90, "x": 3, "y": 1}, {"patternId": "B", "rotation": 270, "x": 2, "y": 1}, {"patternId": "circle", "rotation": 90, "x": 2, "y": 2}, {"patternId": "G", "rotation": 90, "x": 1, "y": 2}, {"patternId": "B", "rotation": 0, "x": 1, "y": 1}, {"patternId": "circle", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["RIGHT", "BACK", "BOTTOM", "LEFT", "FRONT", "BOTTOM", "RIGHT", "FRONT", "BOTTOM"], "required_slots": ["RIGHT", "BACK", "BOTTOM", "LEFT", "FRONT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "circle", "rotation": 270}, "FRONT": {"patternId": "B", "rotation": 90}, "BACK": {"patternId": "F", "rotation": 270}, "LEFT": {"patternId": "P", "rotation": 0}, "RIGHT": {"patternId": "G", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "circle", "rotation": 270}, "FRONT": {"patternId": "B", "rotation": 90}, "BACK": {"patternId": "F", "rotation": 270}, "LEFT": {"patternId": "P", "rotation": 0}, "RIGHT": {"patternId": "G", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C359\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> W -> N -> W -> S -> W -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=G, rotation=270, flipVertical=true\n- step 2: patternId=F, rotation=180, flipVertical=true\n- step 3: patternId=circle, rotation=180, flipVertical=true\n- step 4: patternId=P, rotation=90, flipVertical=true\n- step 5: patternId=B, rotation=270, flipVertical=true\n- step 6: patternId=circle, rotation=90, flipVertical=true\n- step 7: patternId=G, rotation=90, flipVertical=true\n- step 8: patternId=B, rotation=0, flipVertical=true\n- step 9: patternId=circle, rotation=180, flipVertical=true\n- allowed patternId values for this task: G, F, circle, P, B, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C359"} +{"sample_id": "C360", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> W -> S -> E -> S -> N -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "W", "S", "E", "S", "N", "E", "S"], "observed_path_faces": [{"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C360_path_sequence.png"}, "metadata": {"level_id": 360, "name": "Reconstruct 360", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-360.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["X", "K", "A", "H", "smile", "square"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "X", "rotation": 180}, "BOTTOM": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "K", "rotation": 180}, "BACK": {"patternId": "H", "rotation": 90}, "LEFT": {"patternId": "smile", "rotation": 270}, "RIGHT": {"patternId": "A", "rotation": 0}}, "bottom_faces": [{"patternId": "square", "rotation": 90, "x": 3, "y": 1}, {"patternId": "K", "rotation": 180, "x": 3, "y": 2}, {"patternId": "smile", "rotation": 270, "x": 2, "y": 2}, {"patternId": "H", "rotation": 90, "x": 1, "y": 2}, {"patternId": "X", "rotation": 0, "x": 1, "y": 3}, {"patternId": "smile", "rotation": 180, "x": 2, "y": 3}, {"patternId": "K", "rotation": 90, "x": 2, "y": 4}, {"patternId": "smile", "rotation": 180, "x": 2, "y": 3}, {"patternId": "square", "rotation": 90, "x": 3, "y": 3}, {"patternId": "K", "rotation": 180, "x": 3, "y": 4}], "slot_sequence": ["FRONT", "LEFT", "BACK", "TOP", "LEFT", "FRONT", "LEFT", "BOTTOM", "FRONT"], "required_slots": ["FRONT", "LEFT", "BACK", "TOP", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "X", "rotation": 180}, "BOTTOM": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "K", "rotation": 180}, "BACK": {"patternId": "H", "rotation": 270}, "LEFT": {"patternId": "smile", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "X", "rotation": 180}, "BOTTOM": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "K", "rotation": 180}, "BACK": {"patternId": "H", "rotation": 270}, "LEFT": {"patternId": "smile", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C360\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> W -> S -> E -> S -> N -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=K, rotation=180, flipVertical=true\n- step 2: patternId=smile, rotation=270, flipVertical=true\n- step 3: patternId=H, rotation=90, flipVertical=true\n- step 4: patternId=X, rotation=0, flipVertical=true\n- step 5: patternId=smile, rotation=180, flipVertical=true\n- step 6: patternId=K, rotation=90, flipVertical=true\n- step 7: patternId=smile, rotation=180, flipVertical=true\n- step 8: patternId=square, rotation=90, flipVertical=true\n- step 9: patternId=K, rotation=180, flipVertical=true\n- allowed patternId values for this task: K, smile, H, X, square, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C360"} +{"sample_id": "C361", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> S -> S -> S -> N -> W -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "S", "S", "S", "N", "W", "S", "W"], "observed_path_faces": [{"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C361_path_sequence.png"}, "metadata": {"level_id": 361, "name": "Reconstruct 361", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-361.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["T", "C", "triangle", "T", "6", "circle"], "start_x": 2, "start_y": 2, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "T", "rotation": 270}, "BOTTOM": {"patternId": "circle", "rotation": 90}, "FRONT": {"patternId": "C", "rotation": 180}, "BACK": {"patternId": "T", "rotation": 270}, "LEFT": {"patternId": "6", "rotation": 270}, "RIGHT": {"patternId": "triangle", "rotation": 0}}, "bottom_faces": [{"patternId": "circle", "rotation": 90, "x": 2, "y": 2}, {"patternId": "T", "rotation": 90, "x": 2, "y": 1}, {"patternId": "triangle", "rotation": 180, "x": 3, "y": 1}, {"patternId": "circle", "rotation": 180, "x": 3, "y": 2}, {"patternId": "6", "rotation": 270, "x": 3, "y": 3}, {"patternId": "T", "rotation": 180, "x": 3, "y": 4}, {"patternId": "6", "rotation": 270, "x": 3, "y": 3}, {"patternId": "T", "rotation": 270, "x": 2, "y": 3}, {"patternId": "T", "rotation": 90, "x": 2, "y": 4}, {"patternId": "triangle", "rotation": 90, "x": 1, "y": 4}], "slot_sequence": ["BACK", "RIGHT", "BOTTOM", "LEFT", "TOP", "LEFT", "BACK", "TOP", "RIGHT"], "required_slots": ["BACK", "RIGHT", "BOTTOM", "LEFT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "T", "rotation": 270}, "BOTTOM": {"patternId": "circle", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 90}, "LEFT": {"patternId": "6", "rotation": 0}, "RIGHT": {"patternId": "triangle", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "T", "rotation": 270}, "BOTTOM": {"patternId": "circle", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 90}, "LEFT": {"patternId": "6", "rotation": 0}, "RIGHT": {"patternId": "triangle", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C361\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> S -> S -> S -> N -> W -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=T, rotation=90, flipVertical=true\n- step 2: patternId=triangle, rotation=180, flipVertical=true\n- step 3: patternId=circle, rotation=180, flipVertical=true\n- step 4: patternId=6, rotation=270, flipVertical=true\n- step 5: patternId=T, rotation=180, flipVertical=true\n- step 6: patternId=6, rotation=270, flipVertical=true\n- step 7: patternId=T, rotation=270, flipVertical=true\n- step 8: patternId=T, rotation=90, flipVertical=true\n- step 9: patternId=triangle, rotation=90, flipVertical=true\n- allowed patternId values for this task: T, triangle, circle, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C361"} +{"sample_id": "C362", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> N -> N -> W -> W -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "N", "N", "W", "W", "S", "W"], "observed_path_faces": [{"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C362_path_sequence.png"}, "metadata": {"level_id": 362, "name": "Reconstruct 362", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-362.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Q", "8", "circle", "G", "triangle", "W"], "start_x": 6, "start_y": 3, "grid_width": 8, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "Q", "rotation": 180}, "BOTTOM": {"patternId": "W", "rotation": 90}, "FRONT": {"patternId": "8", "rotation": 270}, "BACK": {"patternId": "G", "rotation": 90}, "LEFT": {"patternId": "triangle", "rotation": 180}, "RIGHT": {"patternId": "circle", "rotation": 180}}, "bottom_faces": [{"patternId": "W", "rotation": 90, "x": 6, "y": 3}, {"patternId": "triangle", "rotation": 90, "x": 5, "y": 3}, {"patternId": "Q", "rotation": 0, "x": 4, "y": 3}, {"patternId": "G", "rotation": 90, "x": 4, "y": 2}, {"patternId": "W", "rotation": 270, "x": 4, "y": 1}, {"patternId": "circle", "rotation": 90, "x": 3, "y": 1}, {"patternId": "Q", "rotation": 180, "x": 2, "y": 1}, {"patternId": "G", "rotation": 270, "x": 2, "y": 2}, {"patternId": "triangle", "rotation": 0, "x": 1, "y": 2}], "slot_sequence": ["LEFT", "TOP", "BACK", "BOTTOM", "RIGHT", "TOP", "BACK", "LEFT"], "required_slots": ["LEFT", "TOP", "BACK", "BOTTOM", "RIGHT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "Q", "rotation": 180}, "BOTTOM": {"patternId": "W", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "G", "rotation": 270}, "LEFT": {"patternId": "triangle", "rotation": 270}, "RIGHT": {"patternId": "circle", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "Q", "rotation": 180}, "BOTTOM": {"patternId": "W", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "G", "rotation": 270}, "LEFT": {"patternId": "triangle", "rotation": 270}, "RIGHT": {"patternId": "circle", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C362\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> N -> N -> W -> W -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=triangle, rotation=90, flipVertical=true\n- step 2: patternId=Q, rotation=0, flipVertical=true\n- step 3: patternId=G, rotation=90, flipVertical=true\n- step 4: patternId=W, rotation=270, flipVertical=true\n- step 5: patternId=circle, rotation=90, flipVertical=true\n- step 6: patternId=Q, rotation=180, flipVertical=true\n- step 7: patternId=G, rotation=270, flipVertical=true\n- step 8: patternId=triangle, rotation=0, flipVertical=true\n- allowed patternId values for this task: triangle, Q, G, W, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C362"} +{"sample_id": "C363", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> E -> S -> E -> E -> E -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "E", "S", "E", "E", "E", "S", "E"], "observed_path_faces": [{"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C363_path_sequence.png"}, "metadata": {"level_id": 363, "name": "Reconstruct 363", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-363.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["4", "N", "Q", "E", "9", "U"], "start_x": 1, "start_y": 2, "grid_width": 9, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "4", "rotation": 0}, "BOTTOM": {"patternId": "U", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 270}, "BACK": {"patternId": "E", "rotation": 270}, "LEFT": {"patternId": "9", "rotation": 90}, "RIGHT": {"patternId": "Q", "rotation": 90}}, "bottom_faces": [{"patternId": "U", "rotation": 0, "x": 1, "y": 2}, {"patternId": "Q", "rotation": 180, "x": 2, "y": 2}, {"patternId": "E", "rotation": 0, "x": 2, "y": 1}, {"patternId": "4", "rotation": 270, "x": 3, "y": 1}, {"patternId": "Q", "rotation": 270, "x": 3, "y": 2}, {"patternId": "N", "rotation": 90, "x": 4, "y": 2}, {"patternId": "9", "rotation": 270, "x": 5, "y": 2}, {"patternId": "E", "rotation": 90, "x": 6, "y": 2}, {"patternId": "U", "rotation": 0, "x": 6, "y": 3}, {"patternId": "Q", "rotation": 180, "x": 7, "y": 3}], "slot_sequence": ["RIGHT", "BACK", "TOP", "RIGHT", "FRONT", "LEFT", "BACK", "BOTTOM", "RIGHT"], "required_slots": ["RIGHT", "BACK", "TOP", "FRONT", "LEFT", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "4", "rotation": 0}, "BOTTOM": {"patternId": "U", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 270}, "BACK": {"patternId": "E", "rotation": 90}, "LEFT": {"patternId": "9", "rotation": 180}, "RIGHT": {"patternId": "Q", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "4", "rotation": 0}, "BOTTOM": {"patternId": "U", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 270}, "BACK": {"patternId": "E", "rotation": 90}, "LEFT": {"patternId": "9", "rotation": 180}, "RIGHT": {"patternId": "Q", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C363\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> E -> S -> E -> E -> E -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Q, rotation=180, flipVertical=true\n- step 2: patternId=E, rotation=0, flipVertical=true\n- step 3: patternId=4, rotation=270, flipVertical=true\n- step 4: patternId=Q, rotation=270, flipVertical=true\n- step 5: patternId=N, rotation=90, flipVertical=true\n- step 6: patternId=9, rotation=270, flipVertical=true\n- step 7: patternId=E, rotation=90, flipVertical=true\n- step 8: patternId=U, rotation=0, flipVertical=true\n- step 9: patternId=Q, rotation=180, flipVertical=true\n- allowed patternId values for this task: Q, E, 4, N, 9, U, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C363"} +{"sample_id": "C364", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> N -> W -> N -> W -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "N", "W", "N", "W", "S", "E"], "observed_path_faces": [{"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C364_path_sequence.png"}, "metadata": {"level_id": 364, "name": "Reconstruct 364", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-364.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_left", "arrow_down", "plus", "U", "O", "P"], "start_x": 4, "start_y": 4, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "arrow_left", "rotation": 180}, "BOTTOM": {"patternId": "P", "rotation": 90}, "FRONT": {"patternId": "arrow_down", "rotation": 0}, "BACK": {"patternId": "U", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 90}, "RIGHT": {"patternId": "plus", "rotation": 180}}, "bottom_faces": [{"patternId": "P", "rotation": 90, "x": 4, "y": 4}, {"patternId": "U", "rotation": 180, "x": 4, "y": 3}, {"patternId": "O", "rotation": 270, "x": 3, "y": 3}, {"patternId": "arrow_left", "rotation": 270, "x": 3, "y": 2}, {"patternId": "arrow_down", "rotation": 90, "x": 2, "y": 2}, {"patternId": "plus", "rotation": 270, "x": 2, "y": 1}, {"patternId": "P", "rotation": 90, "x": 1, "y": 1}, {"patternId": "arrow_down", "rotation": 0, "x": 1, "y": 2}, {"patternId": "plus", "rotation": 180, "x": 2, "y": 2}], "slot_sequence": ["BACK", "LEFT", "TOP", "FRONT", "RIGHT", "BOTTOM", "FRONT", "RIGHT"], "required_slots": ["BACK", "LEFT", "TOP", "FRONT", "RIGHT", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "arrow_left", "rotation": 180}, "BOTTOM": {"patternId": "P", "rotation": 90}, "FRONT": {"patternId": "arrow_down", "rotation": 0}, "BACK": {"patternId": "U", "rotation": 180}, "LEFT": {"patternId": "O", "rotation": 180}, "RIGHT": {"patternId": "plus", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "arrow_left", "rotation": 180}, "BOTTOM": {"patternId": "P", "rotation": 90}, "FRONT": {"patternId": "arrow_down", "rotation": 0}, "BACK": {"patternId": "U", "rotation": 180}, "LEFT": {"patternId": "O", "rotation": 180}, "RIGHT": {"patternId": "plus", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C364\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> N -> W -> N -> W -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=U, rotation=180, flipVertical=true\n- step 2: patternId=O, rotation=270, flipVertical=true\n- step 3: patternId=arrow_left, rotation=270, flipVertical=true\n- step 4: patternId=arrow_down, rotation=90, flipVertical=true\n- step 5: patternId=plus, rotation=270, flipVertical=true\n- step 6: patternId=P, rotation=90, flipVertical=true\n- step 7: patternId=arrow_down, rotation=0, flipVertical=true\n- step 8: patternId=plus, rotation=180, flipVertical=true\n- allowed patternId values for this task: U, O, arrow_left, arrow_down, plus, P, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C364"} +{"sample_id": "C365", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> W -> W -> W -> N -> W -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "W", "W", "W", "N", "W", "N", "W"], "observed_path_faces": [{"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C365_path_sequence.png"}, "metadata": {"level_id": 365, "name": "Reconstruct 365", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-365.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["S", "W", "Q", "plus", "G", "triangle"], "start_x": 7, "start_y": 2, "grid_width": 9, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "S", "rotation": 0}, "BOTTOM": {"patternId": "triangle", "rotation": 90}, "FRONT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "plus", "rotation": 90}, "LEFT": {"patternId": "G", "rotation": 270}, "RIGHT": {"patternId": "Q", "rotation": 270}}, "bottom_faces": [{"patternId": "triangle", "rotation": 90, "x": 7, "y": 2}, {"patternId": "G", "rotation": 180, "x": 6, "y": 2}, {"patternId": "W", "rotation": 0, "x": 6, "y": 3}, {"patternId": "S", "rotation": 270, "x": 5, "y": 3}, {"patternId": "plus", "rotation": 180, "x": 4, "y": 3}, {"patternId": "triangle", "rotation": 0, "x": 3, "y": 3}, {"patternId": "G", "rotation": 90, "x": 3, "y": 2}, {"patternId": "W", "rotation": 270, "x": 2, "y": 2}, {"patternId": "S", "rotation": 180, "x": 2, "y": 1}, {"patternId": "Q", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "FRONT", "TOP", "BACK", "BOTTOM", "LEFT", "FRONT", "TOP", "RIGHT"], "required_slots": ["LEFT", "FRONT", "TOP", "BACK", "BOTTOM", "RIGHT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "S", "rotation": 0}, "BOTTOM": {"patternId": "triangle", "rotation": 90}, "FRONT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "plus", "rotation": 270}, "LEFT": {"patternId": "G", "rotation": 0}, "RIGHT": {"patternId": "Q", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 0}, "BOTTOM": {"patternId": "triangle", "rotation": 90}, "FRONT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "plus", "rotation": 270}, "LEFT": {"patternId": "G", "rotation": 0}, "RIGHT": {"patternId": "Q", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C365\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> W -> W -> W -> N -> W -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=G, rotation=180, flipVertical=true\n- step 2: patternId=W, rotation=0, flipVertical=true\n- step 3: patternId=S, rotation=270, flipVertical=true\n- step 4: patternId=plus, rotation=180, flipVertical=true\n- step 5: patternId=triangle, rotation=0, flipVertical=true\n- step 6: patternId=G, rotation=90, flipVertical=true\n- step 7: patternId=W, rotation=270, flipVertical=true\n- step 8: patternId=S, rotation=180, flipVertical=true\n- step 9: patternId=Q, rotation=0, flipVertical=true\n- allowed patternId values for this task: G, W, S, plus, triangle, Q, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C365"} +{"sample_id": "C366", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> N -> N -> E -> N -> N -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "N", "N", "E", "N", "N", "E", "S"], "observed_path_faces": [{"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C366_path_sequence.png"}, "metadata": {"level_id": 366, "name": "Reconstruct 366", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-366.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["I", "2", "6", "K", "J", "F"], "start_x": 3, "start_y": 5, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "I", "rotation": 90}, "BOTTOM": {"patternId": "F", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 90}, "LEFT": {"patternId": "J", "rotation": 270}, "RIGHT": {"patternId": "6", "rotation": 180}}, "bottom_faces": [{"patternId": "F", "rotation": 0, "x": 3, "y": 5}, {"patternId": "J", "rotation": 180, "x": 2, "y": 5}, {"patternId": "I", "rotation": 270, "x": 1, "y": 5}, {"patternId": "K", "rotation": 90, "x": 1, "y": 4}, {"patternId": "F", "rotation": 180, "x": 1, "y": 3}, {"patternId": "J", "rotation": 0, "x": 2, "y": 3}, {"patternId": "2", "rotation": 90, "x": 2, "y": 2}, {"patternId": "6", "rotation": 270, "x": 2, "y": 1}, {"patternId": "I", "rotation": 270, "x": 3, "y": 1}, {"patternId": "2", "rotation": 180, "x": 3, "y": 2}], "slot_sequence": ["LEFT", "TOP", "BACK", "BOTTOM", "LEFT", "FRONT", "RIGHT", "TOP", "FRONT"], "required_slots": ["LEFT", "TOP", "BACK", "BOTTOM", "FRONT", "RIGHT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "I", "rotation": 90}, "BOTTOM": {"patternId": "F", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "J", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 90}, "BOTTOM": {"patternId": "F", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "J", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C366\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> N -> N -> E -> N -> N -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=J, rotation=180, flipVertical=true\n- step 2: patternId=I, rotation=270, flipVertical=true\n- step 3: patternId=K, rotation=90, flipVertical=true\n- step 4: patternId=F, rotation=180, flipVertical=true\n- step 5: patternId=J, rotation=0, flipVertical=true\n- step 6: patternId=2, rotation=90, flipVertical=true\n- step 7: patternId=6, rotation=270, flipVertical=true\n- step 8: patternId=I, rotation=270, flipVertical=true\n- step 9: patternId=2, rotation=180, flipVertical=true\n- allowed patternId values for this task: J, I, K, F, 2, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C366"} +{"sample_id": "C367", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> N -> E -> N -> W -> N -> N -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "N", "E", "N", "W", "N", "N", "E", "S"], "observed_path_faces": [{"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C367_path_sequence.png"}, "metadata": {"level_id": 367, "name": "Reconstruct 367", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-367.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["star", "2", "arrow_right", "T", "G", "1"], "start_x": 1, "start_y": 4, "grid_width": 4, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "star", "rotation": 90}, "BOTTOM": {"patternId": "1", "rotation": 90}, "FRONT": {"patternId": "2", "rotation": 180}, "BACK": {"patternId": "T", "rotation": 0}, "LEFT": {"patternId": "G", "rotation": 270}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}}, "bottom_faces": [{"patternId": "1", "rotation": 90, "x": 1, "y": 4}, {"patternId": "2", "rotation": 180, "x": 1, "y": 5}, {"patternId": "1", "rotation": 90, "x": 1, "y": 4}, {"patternId": "arrow_right", "rotation": 0, "x": 2, "y": 4}, {"patternId": "T", "rotation": 90, "x": 2, "y": 3}, {"patternId": "1", "rotation": 0, "x": 1, "y": 3}, {"patternId": "G", "rotation": 90, "x": 1, "y": 2}, {"patternId": "star", "rotation": 180, "x": 1, "y": 1}, {"patternId": "T", "rotation": 270, "x": 2, "y": 1}, {"patternId": "G", "rotation": 180, "x": 2, "y": 2}], "slot_sequence": ["FRONT", "BOTTOM", "RIGHT", "BACK", "BOTTOM", "LEFT", "TOP", "BACK", "LEFT"], "required_slots": ["FRONT", "BOTTOM", "RIGHT", "BACK", "LEFT", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "star", "rotation": 90}, "BOTTOM": {"patternId": "1", "rotation": 90}, "FRONT": {"patternId": "2", "rotation": 180}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "G", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 90}, "BOTTOM": {"patternId": "1", "rotation": 90}, "FRONT": {"patternId": "2", "rotation": 180}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "G", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C367\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> N -> E -> N -> W -> N -> N -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=2, rotation=180, flipVertical=true\n- step 2: patternId=1, rotation=90, flipVertical=true\n- step 3: patternId=arrow_right, rotation=0, flipVertical=true\n- step 4: patternId=T, rotation=90, flipVertical=true\n- step 5: patternId=1, rotation=0, flipVertical=true\n- step 6: patternId=G, rotation=90, flipVertical=true\n- step 7: patternId=star, rotation=180, flipVertical=true\n- step 8: patternId=T, rotation=270, flipVertical=true\n- step 9: patternId=G, rotation=180, flipVertical=true\n- allowed patternId values for this task: 2, 1, arrow_right, T, G, star, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C367"} +{"sample_id": "C368", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> N -> N -> E -> S -> E -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "N", "N", "E", "S", "E", "N", "E"], "observed_path_faces": [{"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C368_path_sequence.png"}, "metadata": {"level_id": 368, "name": "Reconstruct 368", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-368.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["4", "O", "plus", "R", "O", "arrow_up"], "start_x": 1, "start_y": 2, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "4", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "O", "rotation": 180}, "BACK": {"patternId": "R", "rotation": 90}, "LEFT": {"patternId": "O", "rotation": 0}, "RIGHT": {"patternId": "plus", "rotation": 180}}, "bottom_faces": [{"patternId": "arrow_up", "rotation": 270, "x": 1, "y": 2}, {"patternId": "O", "rotation": 180, "x": 1, "y": 3}, {"patternId": "plus", "rotation": 180, "x": 2, "y": 3}, {"patternId": "arrow_up", "rotation": 180, "x": 2, "y": 2}, {"patternId": "O", "rotation": 180, "x": 2, "y": 1}, {"patternId": "R", "rotation": 270, "x": 3, "y": 1}, {"patternId": "arrow_up", "rotation": 270, "x": 3, "y": 2}, {"patternId": "plus", "rotation": 270, "x": 4, "y": 2}, {"patternId": "R", "rotation": 180, "x": 4, "y": 1}, {"patternId": "4", "rotation": 270, "x": 5, "y": 1}], "slot_sequence": ["FRONT", "RIGHT", "BOTTOM", "LEFT", "BACK", "BOTTOM", "RIGHT", "BACK", "TOP"], "required_slots": ["FRONT", "RIGHT", "BOTTOM", "LEFT", "BACK", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "4", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "O", "rotation": 180}, "BACK": {"patternId": "R", "rotation": 270}, "LEFT": {"patternId": "O", "rotation": 90}, "RIGHT": {"patternId": "plus", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "4", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "O", "rotation": 180}, "BACK": {"patternId": "R", "rotation": 270}, "LEFT": {"patternId": "O", "rotation": 90}, "RIGHT": {"patternId": "plus", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C368\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> N -> N -> E -> S -> E -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=O, rotation=180, flipVertical=true\n- step 2: patternId=plus, rotation=180, flipVertical=true\n- step 3: patternId=arrow_up, rotation=180, flipVertical=true\n- step 4: patternId=O, rotation=180, flipVertical=true\n- step 5: patternId=R, rotation=270, flipVertical=true\n- step 6: patternId=arrow_up, rotation=270, flipVertical=true\n- step 7: patternId=plus, rotation=270, flipVertical=true\n- step 8: patternId=R, rotation=180, flipVertical=true\n- step 9: patternId=4, rotation=270, flipVertical=true\n- allowed patternId values for this task: O, plus, arrow_up, R, 4, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C368"} +{"sample_id": "C369", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> W -> E -> E -> N -> W -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "W", "E", "E", "N", "W", "W", "W"], "observed_path_faces": [{"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C369_path_sequence.png"}, "metadata": {"level_id": 369, "name": "Reconstruct 369", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-369.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_down", "I", "3", "Q", "arrow_down", "2"], "start_x": 3, "start_y": 1, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "arrow_down", "rotation": 0}, "BOTTOM": {"patternId": "2", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 90}, "BACK": {"patternId": "Q", "rotation": 90}, "LEFT": {"patternId": "arrow_down", "rotation": 0}, "RIGHT": {"patternId": "3", "rotation": 0}}, "bottom_faces": [{"patternId": "2", "rotation": 0, "x": 3, "y": 1}, {"patternId": "I", "rotation": 90, "x": 3, "y": 2}, {"patternId": "arrow_down", "rotation": 0, "x": 3, "y": 3}, {"patternId": "arrow_down", "rotation": 90, "x": 2, "y": 3}, {"patternId": "arrow_down", "rotation": 0, "x": 3, "y": 3}, {"patternId": "3", "rotation": 270, "x": 4, "y": 3}, {"patternId": "I", "rotation": 0, "x": 4, "y": 2}, {"patternId": "arrow_down", "rotation": 270, "x": 3, "y": 2}, {"patternId": "Q", "rotation": 180, "x": 2, "y": 2}, {"patternId": "2", "rotation": 270, "x": 1, "y": 2}], "slot_sequence": ["FRONT", "TOP", "LEFT", "TOP", "RIGHT", "FRONT", "TOP", "BACK", "BOTTOM"], "required_slots": ["FRONT", "TOP", "LEFT", "RIGHT", "BACK", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "arrow_down", "rotation": 0}, "BOTTOM": {"patternId": "2", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 90}, "BACK": {"patternId": "Q", "rotation": 270}, "LEFT": {"patternId": "arrow_down", "rotation": 90}, "RIGHT": {"patternId": "3", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "arrow_down", "rotation": 0}, "BOTTOM": {"patternId": "2", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 90}, "BACK": {"patternId": "Q", "rotation": 270}, "LEFT": {"patternId": "arrow_down", "rotation": 90}, "RIGHT": {"patternId": "3", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C369\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> W -> E -> E -> N -> W -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=I, rotation=90, flipVertical=true\n- step 2: patternId=arrow_down, rotation=0, flipVertical=true\n- step 3: patternId=arrow_down, rotation=90, flipVertical=true\n- step 4: patternId=arrow_down, rotation=0, flipVertical=true\n- step 5: patternId=3, rotation=270, flipVertical=true\n- step 6: patternId=I, rotation=0, flipVertical=true\n- step 7: patternId=arrow_down, rotation=270, flipVertical=true\n- step 8: patternId=Q, rotation=180, flipVertical=true\n- step 9: patternId=2, rotation=270, flipVertical=true\n- allowed patternId values for this task: I, arrow_down, 3, Q, 2, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C369"} +{"sample_id": "C370", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> E -> W -> S -> W -> E -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "E", "W", "S", "W", "E", "W", "W"], "observed_path_faces": [{"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C370_path_sequence.png"}, "metadata": {"level_id": 370, "name": "Reconstruct 370", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-370.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["O", "K", "diamond", "2", "T", "1"], "start_x": 3, "start_y": 1, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "1", "rotation": 90}, "FRONT": {"patternId": "K", "rotation": 90}, "BACK": {"patternId": "2", "rotation": 270}, "LEFT": {"patternId": "T", "rotation": 90}, "RIGHT": {"patternId": "diamond", "rotation": 180}}, "bottom_faces": [{"patternId": "1", "rotation": 90, "x": 3, "y": 1}, {"patternId": "K", "rotation": 90, "x": 3, "y": 2}, {"patternId": "O", "rotation": 270, "x": 3, "y": 3}, {"patternId": "diamond", "rotation": 90, "x": 4, "y": 3}, {"patternId": "O", "rotation": 270, "x": 3, "y": 3}, {"patternId": "2", "rotation": 90, "x": 3, "y": 4}, {"patternId": "T", "rotation": 270, "x": 2, "y": 4}, {"patternId": "2", "rotation": 90, "x": 3, "y": 4}, {"patternId": "T", "rotation": 270, "x": 2, "y": 4}, {"patternId": "K", "rotation": 270, "x": 1, "y": 4}], "slot_sequence": ["FRONT", "TOP", "RIGHT", "TOP", "BACK", "LEFT", "BACK", "LEFT", "FRONT"], "required_slots": ["FRONT", "TOP", "RIGHT", "BACK", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "K", "rotation": 90}, "BACK": {"patternId": "2", "rotation": 90}, "LEFT": {"patternId": "T", "rotation": 180}, "RIGHT": {"patternId": "diamond", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "K", "rotation": 90}, "BACK": {"patternId": "2", "rotation": 90}, "LEFT": {"patternId": "T", "rotation": 180}, "RIGHT": {"patternId": "diamond", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C370\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> E -> W -> S -> W -> E -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=K, rotation=90, flipVertical=true\n- step 2: patternId=O, rotation=270, flipVertical=true\n- step 3: patternId=diamond, rotation=90, flipVertical=true\n- step 4: patternId=O, rotation=270, flipVertical=true\n- step 5: patternId=2, rotation=90, flipVertical=true\n- step 6: patternId=T, rotation=270, flipVertical=true\n- step 7: patternId=2, rotation=90, flipVertical=true\n- step 8: patternId=T, rotation=270, flipVertical=true\n- step 9: patternId=K, rotation=270, flipVertical=true\n- allowed patternId values for this task: K, O, diamond, 2, T, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C370"} +{"sample_id": "C371", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> S -> S -> E -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "W", "S", "S", "E", "W", "N"], "observed_path_faces": [{"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C371_path_sequence.png"}, "metadata": {"level_id": 371, "name": "Reconstruct 371", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-371.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_left", "star", "T", "8", "3", "U"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "arrow_left", "rotation": 270}, "BOTTOM": {"patternId": "U", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 90}, "BACK": {"patternId": "8", "rotation": 270}, "LEFT": {"patternId": "3", "rotation": 270}, "RIGHT": {"patternId": "T", "rotation": 0}}, "bottom_faces": [{"patternId": "U", "rotation": 0, "x": 1, "y": 1}, {"patternId": "T", "rotation": 90, "x": 2, "y": 1}, {"patternId": "star", "rotation": 180, "x": 2, "y": 2}, {"patternId": "U", "rotation": 90, "x": 1, "y": 2}, {"patternId": "3", "rotation": 270, "x": 1, "y": 3}, {"patternId": "arrow_left", "rotation": 180, "x": 1, "y": 4}, {"patternId": "star", "rotation": 0, "x": 2, "y": 4}, {"patternId": "arrow_left", "rotation": 180, "x": 1, "y": 4}, {"patternId": "3", "rotation": 270, "x": 1, "y": 3}], "slot_sequence": ["RIGHT", "FRONT", "BOTTOM", "LEFT", "TOP", "FRONT", "TOP", "LEFT"], "required_slots": ["RIGHT", "FRONT", "BOTTOM", "LEFT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "arrow_left", "rotation": 270}, "BOTTOM": {"patternId": "U", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 0}, "RIGHT": {"patternId": "T", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "arrow_left", "rotation": 270}, "BOTTOM": {"patternId": "U", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 0}, "RIGHT": {"patternId": "T", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C371\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> S -> S -> E -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=T, rotation=90, flipVertical=true\n- step 2: patternId=star, rotation=180, flipVertical=true\n- step 3: patternId=U, rotation=90, flipVertical=true\n- step 4: patternId=3, rotation=270, flipVertical=true\n- step 5: patternId=arrow_left, rotation=180, flipVertical=true\n- step 6: patternId=star, rotation=0, flipVertical=true\n- step 7: patternId=arrow_left, rotation=180, flipVertical=true\n- step 8: patternId=3, rotation=270, flipVertical=true\n- allowed patternId values for this task: T, star, U, 3, arrow_left, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C371"} +{"sample_id": "C372", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> N -> N -> W -> W -> S -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "N", "N", "W", "W", "S", "E", "E"], "observed_path_faces": [{"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C372_path_sequence.png"}, "metadata": {"level_id": 372, "name": "Reconstruct 372", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-372.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_down", "L", "heart", "arrow_right", "triangle", "R"], "start_x": 4, "start_y": 4, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "arrow_down", "rotation": 180}, "BOTTOM": {"patternId": "R", "rotation": 180}, "FRONT": {"patternId": "L", "rotation": 270}, "BACK": {"patternId": "arrow_right", "rotation": 270}, "LEFT": {"patternId": "triangle", "rotation": 270}, "RIGHT": {"patternId": "heart", "rotation": 0}}, "bottom_faces": [{"patternId": "R", "rotation": 180, "x": 4, "y": 4}, {"patternId": "arrow_right", "rotation": 90, "x": 4, "y": 3}, {"patternId": "triangle", "rotation": 90, "x": 3, "y": 3}, {"patternId": "arrow_down", "rotation": 270, "x": 3, "y": 2}, {"patternId": "heart", "rotation": 0, "x": 3, "y": 1}, {"patternId": "L", "rotation": 270, "x": 2, "y": 1}, {"patternId": "triangle", "rotation": 270, "x": 1, "y": 1}, {"patternId": "arrow_down", "rotation": 90, "x": 1, "y": 2}, {"patternId": "L", "rotation": 180, "x": 2, "y": 2}, {"patternId": "R", "rotation": 90, "x": 3, "y": 2}], "slot_sequence": ["BACK", "LEFT", "TOP", "RIGHT", "FRONT", "LEFT", "TOP", "FRONT", "BOTTOM"], "required_slots": ["BACK", "LEFT", "TOP", "RIGHT", "FRONT", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "arrow_down", "rotation": 180}, "BOTTOM": {"patternId": "R", "rotation": 180}, "FRONT": {"patternId": "L", "rotation": 270}, "BACK": {"patternId": "arrow_right", "rotation": 90}, "LEFT": {"patternId": "triangle", "rotation": 0}, "RIGHT": {"patternId": "heart", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "arrow_down", "rotation": 180}, "BOTTOM": {"patternId": "R", "rotation": 180}, "FRONT": {"patternId": "L", "rotation": 270}, "BACK": {"patternId": "arrow_right", "rotation": 90}, "LEFT": {"patternId": "triangle", "rotation": 0}, "RIGHT": {"patternId": "heart", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C372\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> N -> N -> W -> W -> S -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_right, rotation=90, flipVertical=true\n- step 2: patternId=triangle, rotation=90, flipVertical=true\n- step 3: patternId=arrow_down, rotation=270, flipVertical=true\n- step 4: patternId=heart, rotation=0, flipVertical=true\n- step 5: patternId=L, rotation=270, flipVertical=true\n- step 6: patternId=triangle, rotation=270, flipVertical=true\n- step 7: patternId=arrow_down, rotation=90, flipVertical=true\n- step 8: patternId=L, rotation=180, flipVertical=true\n- step 9: patternId=R, rotation=90, flipVertical=true\n- allowed patternId values for this task: arrow_right, triangle, arrow_down, heart, L, R, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C372"} +{"sample_id": "C373", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> E -> E -> S -> E -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "E", "E", "S", "E", "S", "E"], "observed_path_faces": [{"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C373_path_sequence.png"}, "metadata": {"level_id": 373, "name": "Reconstruct 373", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-373.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["H", "circle", "V", "L", "M", "O"], "start_x": 2, "start_y": 1, "grid_width": 7, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "H", "rotation": 180}, "BOTTOM": {"patternId": "O", "rotation": 0}, "FRONT": {"patternId": "circle", "rotation": 0}, "BACK": {"patternId": "L", "rotation": 180}, "LEFT": {"patternId": "M", "rotation": 0}, "RIGHT": {"patternId": "V", "rotation": 180}}, "bottom_faces": [{"patternId": "O", "rotation": 0, "x": 2, "y": 1}, {"patternId": "circle", "rotation": 0, "x": 2, "y": 2}, {"patternId": "M", "rotation": 0, "x": 1, "y": 2}, {"patternId": "circle", "rotation": 0, "x": 2, "y": 2}, {"patternId": "V", "rotation": 180, "x": 3, "y": 2}, {"patternId": "H", "rotation": 270, "x": 3, "y": 3}, {"patternId": "L", "rotation": 90, "x": 4, "y": 3}, {"patternId": "M", "rotation": 270, "x": 4, "y": 4}, {"patternId": "O", "rotation": 0, "x": 5, "y": 4}], "slot_sequence": ["FRONT", "LEFT", "FRONT", "RIGHT", "TOP", "BACK", "LEFT", "BOTTOM"], "required_slots": ["FRONT", "LEFT", "RIGHT", "TOP", "BACK", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "H", "rotation": 180}, "BOTTOM": {"patternId": "O", "rotation": 0}, "FRONT": {"patternId": "circle", "rotation": 0}, "BACK": {"patternId": "L", "rotation": 0}, "LEFT": {"patternId": "M", "rotation": 90}, "RIGHT": {"patternId": "V", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "H", "rotation": 180}, "BOTTOM": {"patternId": "O", "rotation": 0}, "FRONT": {"patternId": "circle", "rotation": 0}, "BACK": {"patternId": "L", "rotation": 0}, "LEFT": {"patternId": "M", "rotation": 90}, "RIGHT": {"patternId": "V", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C373\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> E -> E -> S -> E -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=circle, rotation=0, flipVertical=true\n- step 2: patternId=M, rotation=0, flipVertical=true\n- step 3: patternId=circle, rotation=0, flipVertical=true\n- step 4: patternId=V, rotation=180, flipVertical=true\n- step 5: patternId=H, rotation=270, flipVertical=true\n- step 6: patternId=L, rotation=90, flipVertical=true\n- step 7: patternId=M, rotation=270, flipVertical=true\n- step 8: patternId=O, rotation=0, flipVertical=true\n- allowed patternId values for this task: circle, M, V, H, L, O, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C373"} +{"sample_id": "C374", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> W -> S -> N -> N -> E -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "W", "S", "N", "N", "E", "E", "N"], "observed_path_faces": [{"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C374_path_sequence.png"}, "metadata": {"level_id": 374, "name": "Reconstruct 374", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-374.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["1", "V", "U", "4", "H", "P"], "start_x": 3, "start_y": 4, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "1", "rotation": 0}, "BOTTOM": {"patternId": "P", "rotation": 0}, "FRONT": {"patternId": "V", "rotation": 0}, "BACK": {"patternId": "4", "rotation": 90}, "LEFT": {"patternId": "H", "rotation": 180}, "RIGHT": {"patternId": "U", "rotation": 180}}, "bottom_faces": [{"patternId": "P", "rotation": 0, "x": 3, "y": 4}, {"patternId": "4", "rotation": 270, "x": 3, "y": 3}, {"patternId": "H", "rotation": 0, "x": 2, "y": 3}, {"patternId": "V", "rotation": 180, "x": 1, "y": 3}, {"patternId": "P", "rotation": 180, "x": 1, "y": 4}, {"patternId": "V", "rotation": 180, "x": 1, "y": 3}, {"patternId": "1", "rotation": 180, "x": 1, "y": 2}, {"patternId": "H", "rotation": 90, "x": 2, "y": 2}, {"patternId": "P", "rotation": 0, "x": 3, "y": 2}, {"patternId": "4", "rotation": 270, "x": 3, "y": 1}], "slot_sequence": ["BACK", "LEFT", "FRONT", "BOTTOM", "FRONT", "TOP", "LEFT", "BOTTOM", "BACK"], "required_slots": ["BACK", "LEFT", "FRONT", "BOTTOM", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "1", "rotation": 0}, "BOTTOM": {"patternId": "P", "rotation": 0}, "FRONT": {"patternId": "V", "rotation": 0}, "BACK": {"patternId": "4", "rotation": 270}, "LEFT": {"patternId": "H", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "1", "rotation": 0}, "BOTTOM": {"patternId": "P", "rotation": 0}, "FRONT": {"patternId": "V", "rotation": 0}, "BACK": {"patternId": "4", "rotation": 270}, "LEFT": {"patternId": "H", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C374\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> W -> S -> N -> N -> E -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=4, rotation=270, flipVertical=true\n- step 2: patternId=H, rotation=0, flipVertical=true\n- step 3: patternId=V, rotation=180, flipVertical=true\n- step 4: patternId=P, rotation=180, flipVertical=true\n- step 5: patternId=V, rotation=180, flipVertical=true\n- step 6: patternId=1, rotation=180, flipVertical=true\n- step 7: patternId=H, rotation=90, flipVertical=true\n- step 8: patternId=P, rotation=0, flipVertical=true\n- step 9: patternId=4, rotation=270, flipVertical=true\n- allowed patternId values for this task: 4, H, V, P, 1, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C374"} +{"sample_id": "C375", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> S -> S -> E -> N -> E -> S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "S", "S", "E", "N", "E", "S", "N"], "observed_path_faces": [{"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C375_path_sequence.png"}, "metadata": {"level_id": 375, "name": "Reconstruct 375", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-375.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["plus", "5", "I", "B", "9", "5"], "start_x": 1, "start_y": 2, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "plus", "rotation": 90}, "BOTTOM": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "5", "rotation": 90}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "9", "rotation": 270}, "RIGHT": {"patternId": "I", "rotation": 180}}, "bottom_faces": [{"patternId": "5", "rotation": 90, "x": 1, "y": 2}, {"patternId": "B", "rotation": 180, "x": 1, "y": 1}, {"patternId": "5", "rotation": 90, "x": 1, "y": 2}, {"patternId": "5", "rotation": 90, "x": 1, "y": 3}, {"patternId": "I", "rotation": 180, "x": 2, "y": 3}, {"patternId": "5", "rotation": 0, "x": 2, "y": 2}, {"patternId": "B", "rotation": 90, "x": 3, "y": 2}, {"patternId": "I", "rotation": 270, "x": 3, "y": 3}, {"patternId": "B", "rotation": 90, "x": 3, "y": 2}], "slot_sequence": ["BACK", "BOTTOM", "FRONT", "RIGHT", "BOTTOM", "BACK", "RIGHT", "BACK"], "required_slots": ["BACK", "BOTTOM", "FRONT", "RIGHT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "5", "rotation": 90}, "BACK": {"patternId": "B", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "5", "rotation": 90}, "BACK": {"patternId": "B", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C375\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): N -> S -> S -> E -> N -> E -> S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=B, rotation=180, flipVertical=true\n- step 2: patternId=5, rotation=90, flipVertical=true\n- step 3: patternId=5, rotation=90, flipVertical=true\n- step 4: patternId=I, rotation=180, flipVertical=true\n- step 5: patternId=5, rotation=0, flipVertical=true\n- step 6: patternId=B, rotation=90, flipVertical=true\n- step 7: patternId=I, rotation=270, flipVertical=true\n- step 8: patternId=B, rotation=90, flipVertical=true\n- allowed patternId values for this task: B, 5, I, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C375"} +{"sample_id": "C376", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> E -> N -> W -> E -> W -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "E", "N", "W", "E", "W", "S", "S"], "observed_path_faces": [{"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C376_path_sequence.png"}, "metadata": {"level_id": 376, "name": "Reconstruct 376", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-376.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["F", "plus", "8", "6", "heart", "P"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "F", "rotation": 0}, "BOTTOM": {"patternId": "P", "rotation": 270}, "FRONT": {"patternId": "plus", "rotation": 90}, "BACK": {"patternId": "6", "rotation": 270}, "LEFT": {"patternId": "heart", "rotation": 180}, "RIGHT": {"patternId": "8", "rotation": 0}}, "bottom_faces": [{"patternId": "P", "rotation": 270, "x": 1, "y": 1}, {"patternId": "8", "rotation": 90, "x": 2, "y": 1}, {"patternId": "plus", "rotation": 180, "x": 2, "y": 2}, {"patternId": "F", "rotation": 90, "x": 3, "y": 2}, {"patternId": "8", "rotation": 0, "x": 3, "y": 1}, {"patternId": "plus", "rotation": 90, "x": 2, "y": 1}, {"patternId": "8", "rotation": 0, "x": 3, "y": 1}, {"patternId": "plus", "rotation": 90, "x": 2, "y": 1}, {"patternId": "F", "rotation": 0, "x": 2, "y": 2}, {"patternId": "6", "rotation": 90, "x": 2, "y": 3}], "slot_sequence": ["RIGHT", "FRONT", "TOP", "RIGHT", "FRONT", "RIGHT", "FRONT", "TOP", "BACK"], "required_slots": ["RIGHT", "FRONT", "TOP", "BACK"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "F", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "plus", "rotation": 90}, "BACK": {"patternId": "6", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "8", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "F", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "plus", "rotation": 90}, "BACK": {"patternId": "6", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "8", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C376\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> E -> N -> W -> E -> W -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=8, rotation=90, flipVertical=true\n- step 2: patternId=plus, rotation=180, flipVertical=true\n- step 3: patternId=F, rotation=90, flipVertical=true\n- step 4: patternId=8, rotation=0, flipVertical=true\n- step 5: patternId=plus, rotation=90, flipVertical=true\n- step 6: patternId=8, rotation=0, flipVertical=true\n- step 7: patternId=plus, rotation=90, flipVertical=true\n- step 8: patternId=F, rotation=0, flipVertical=true\n- step 9: patternId=6, rotation=90, flipVertical=true\n- allowed patternId values for this task: 8, plus, F, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C376"} +{"sample_id": "C377", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> E -> N -> N -> N -> S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "E", "N", "N", "N", "S", "N"], "observed_path_faces": [{"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C377_path_sequence.png"}, "metadata": {"level_id": 377, "name": "Reconstruct 377", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-377.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["E", "6", "B", "1", "A", "2"], "start_x": 1, "start_y": 2, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "E", "rotation": 0}, "BOTTOM": {"patternId": "2", "rotation": 90}, "FRONT": {"patternId": "6", "rotation": 270}, "BACK": {"patternId": "1", "rotation": 0}, "LEFT": {"patternId": "A", "rotation": 270}, "RIGHT": {"patternId": "B", "rotation": 0}}, "bottom_faces": [{"patternId": "2", "rotation": 90, "x": 1, "y": 2}, {"patternId": "6", "rotation": 270, "x": 1, "y": 3}, {"patternId": "E", "rotation": 0, "x": 1, "y": 4}, {"patternId": "B", "rotation": 270, "x": 2, "y": 4}, {"patternId": "6", "rotation": 180, "x": 2, "y": 3}, {"patternId": "A", "rotation": 180, "x": 2, "y": 2}, {"patternId": "1", "rotation": 270, "x": 2, "y": 1}, {"patternId": "A", "rotation": 180, "x": 2, "y": 2}, {"patternId": "1", "rotation": 270, "x": 2, "y": 1}], "slot_sequence": ["FRONT", "TOP", "RIGHT", "FRONT", "LEFT", "BACK", "LEFT", "BACK"], "required_slots": ["FRONT", "TOP", "RIGHT", "LEFT", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "E", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "6", "rotation": 270}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "A", "rotation": 0}, "RIGHT": {"patternId": "B", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "E", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "6", "rotation": 270}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "A", "rotation": 0}, "RIGHT": {"patternId": "B", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C377\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> E -> N -> N -> N -> S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=6, rotation=270, flipVertical=true\n- step 2: patternId=E, rotation=0, flipVertical=true\n- step 3: patternId=B, rotation=270, flipVertical=true\n- step 4: patternId=6, rotation=180, flipVertical=true\n- step 5: patternId=A, rotation=180, flipVertical=true\n- step 6: patternId=1, rotation=270, flipVertical=true\n- step 7: patternId=A, rotation=180, flipVertical=true\n- step 8: patternId=1, rotation=270, flipVertical=true\n- allowed patternId values for this task: 6, E, B, A, 1, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C377"} +{"sample_id": "C378", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> N -> N -> W -> N -> E -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "N", "N", "W", "N", "E", "E", "S"], "observed_path_faces": [{"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C378_path_sequence.png"}, "metadata": {"level_id": 378, "name": "Reconstruct 378", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-378.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["6", "5", "O", "T", "Y", "8"], "start_x": 1, "start_y": 5, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "6", "rotation": 180}, "BOTTOM": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "5", "rotation": 180}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "Y", "rotation": 180}, "RIGHT": {"patternId": "O", "rotation": 90}}, "bottom_faces": [{"patternId": "8", "rotation": 180, "x": 1, "y": 5}, {"patternId": "O", "rotation": 180, "x": 2, "y": 5}, {"patternId": "T", "rotation": 270, "x": 2, "y": 4}, {"patternId": "Y", "rotation": 270, "x": 2, "y": 3}, {"patternId": "5", "rotation": 270, "x": 2, "y": 2}, {"patternId": "8", "rotation": 270, "x": 1, "y": 2}, {"patternId": "O", "rotation": 270, "x": 1, "y": 1}, {"patternId": "5", "rotation": 0, "x": 2, "y": 1}, {"patternId": "Y", "rotation": 0, "x": 3, "y": 1}, {"patternId": "8", "rotation": 90, "x": 3, "y": 2}], "slot_sequence": ["RIGHT", "BACK", "LEFT", "FRONT", "BOTTOM", "RIGHT", "FRONT", "LEFT", "BOTTOM"], "required_slots": ["RIGHT", "BACK", "LEFT", "FRONT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "5", "rotation": 180}, "BACK": {"patternId": "T", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 270}, "RIGHT": {"patternId": "O", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "5", "rotation": 180}, "BACK": {"patternId": "T", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 270}, "RIGHT": {"patternId": "O", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C378\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> N -> N -> W -> N -> E -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=O, rotation=180, flipVertical=true\n- step 2: patternId=T, rotation=270, flipVertical=true\n- step 3: patternId=Y, rotation=270, flipVertical=true\n- step 4: patternId=5, rotation=270, flipVertical=true\n- step 5: patternId=8, rotation=270, flipVertical=true\n- step 6: patternId=O, rotation=270, flipVertical=true\n- step 7: patternId=5, rotation=0, flipVertical=true\n- step 8: patternId=Y, rotation=0, flipVertical=true\n- step 9: patternId=8, rotation=90, flipVertical=true\n- allowed patternId values for this task: O, T, Y, 5, 8, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C378"} +{"sample_id": "C379", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> N -> S -> N -> W -> W -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "N", "S", "N", "W", "W", "N", "N"], "observed_path_faces": [{"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C379_path_sequence.png"}, "metadata": {"level_id": 379, "name": "Reconstruct 379", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-379.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["F", "B", "S", "heart", "M", "V"], "start_x": 4, "start_y": 5, "grid_width": 6, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "F", "rotation": 90}, "BOTTOM": {"patternId": "V", "rotation": 90}, "FRONT": {"patternId": "B", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 180}, "LEFT": {"patternId": "M", "rotation": 90}, "RIGHT": {"patternId": "S", "rotation": 90}}, "bottom_faces": [{"patternId": "V", "rotation": 90, "x": 4, "y": 5}, {"patternId": "heart", "rotation": 0, "x": 4, "y": 4}, {"patternId": "M", "rotation": 270, "x": 3, "y": 4}, {"patternId": "F", "rotation": 180, "x": 3, "y": 3}, {"patternId": "M", "rotation": 270, "x": 3, "y": 4}, {"patternId": "F", "rotation": 180, "x": 3, "y": 3}, {"patternId": "B", "rotation": 90, "x": 2, "y": 3}, {"patternId": "V", "rotation": 180, "x": 1, "y": 3}, {"patternId": "S", "rotation": 270, "x": 1, "y": 2}, {"patternId": "F", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["BACK", "LEFT", "TOP", "LEFT", "TOP", "FRONT", "BOTTOM", "RIGHT", "TOP"], "required_slots": ["BACK", "LEFT", "TOP", "FRONT", "BOTTOM", "RIGHT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "F", "rotation": 90}, "BOTTOM": {"patternId": "V", "rotation": 90}, "FRONT": {"patternId": "B", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 0}, "LEFT": {"patternId": "M", "rotation": 180}, "RIGHT": {"patternId": "S", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "F", "rotation": 90}, "BOTTOM": {"patternId": "V", "rotation": 90}, "FRONT": {"patternId": "B", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 0}, "LEFT": {"patternId": "M", "rotation": 180}, "RIGHT": {"patternId": "S", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C379\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> N -> S -> N -> W -> W -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=heart, rotation=0, flipVertical=true\n- step 2: patternId=M, rotation=270, flipVertical=true\n- step 3: patternId=F, rotation=180, flipVertical=true\n- step 4: patternId=M, rotation=270, flipVertical=true\n- step 5: patternId=F, rotation=180, flipVertical=true\n- step 6: patternId=B, rotation=90, flipVertical=true\n- step 7: patternId=V, rotation=180, flipVertical=true\n- step 8: patternId=S, rotation=270, flipVertical=true\n- step 9: patternId=F, rotation=0, flipVertical=true\n- allowed patternId values for this task: heart, M, F, B, V, S, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C379"} +{"sample_id": "C380", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> E -> S -> W -> W -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "E", "S", "W", "W", "S", "E"], "observed_path_faces": [{"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C380_path_sequence.png"}, "metadata": {"level_id": 380, "name": "Reconstruct 380", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-380.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["X", "diamond", "F", "6", "4", "X"], "start_x": 2, "start_y": 3, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "X", "rotation": 90}, "BOTTOM": {"patternId": "X", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 0}, "BACK": {"patternId": "6", "rotation": 90}, "LEFT": {"patternId": "4", "rotation": 180}, "RIGHT": {"patternId": "F", "rotation": 270}}, "bottom_faces": [{"patternId": "X", "rotation": 0, "x": 2, "y": 3}, {"patternId": "6", "rotation": 270, "x": 2, "y": 2}, {"patternId": "X", "rotation": 90, "x": 2, "y": 1}, {"patternId": "F", "rotation": 180, "x": 3, "y": 1}, {"patternId": "6", "rotation": 0, "x": 3, "y": 2}, {"patternId": "X", "rotation": 180, "x": 2, "y": 2}, {"patternId": "diamond", "rotation": 90, "x": 1, "y": 2}, {"patternId": "4", "rotation": 270, "x": 1, "y": 3}, {"patternId": "X", "rotation": 90, "x": 2, "y": 3}], "slot_sequence": ["BACK", "TOP", "RIGHT", "BACK", "TOP", "FRONT", "LEFT", "TOP"], "required_slots": ["BACK", "TOP", "RIGHT", "FRONT", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "X", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 0}, "BACK": {"patternId": "6", "rotation": 270}, "LEFT": {"patternId": "4", "rotation": 270}, "RIGHT": {"patternId": "F", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "X", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 0}, "BACK": {"patternId": "6", "rotation": 270}, "LEFT": {"patternId": "4", "rotation": 270}, "RIGHT": {"patternId": "F", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C380\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> E -> S -> W -> W -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=6, rotation=270, flipVertical=true\n- step 2: patternId=X, rotation=90, flipVertical=true\n- step 3: patternId=F, rotation=180, flipVertical=true\n- step 4: patternId=6, rotation=0, flipVertical=true\n- step 5: patternId=X, rotation=180, flipVertical=true\n- step 6: patternId=diamond, rotation=90, flipVertical=true\n- step 7: patternId=4, rotation=270, flipVertical=true\n- step 8: patternId=X, rotation=90, flipVertical=true\n- allowed patternId values for this task: 6, X, F, diamond, 4, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C380"} +{"sample_id": "C381", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> N -> W -> N -> E -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "N", "W", "N", "E", "W", "N"], "observed_path_faces": [{"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C381_path_sequence.png"}, "metadata": {"level_id": 381, "name": "Reconstruct 381", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-381.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["C", "E", "X", "5", "B", "A"], "start_x": 2, "start_y": 6, "grid_width": 4, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "C", "rotation": 90}, "BOTTOM": {"patternId": "A", "rotation": 90}, "FRONT": {"patternId": "E", "rotation": 0}, "BACK": {"patternId": "5", "rotation": 0}, "LEFT": {"patternId": "B", "rotation": 90}, "RIGHT": {"patternId": "X", "rotation": 90}}, "bottom_faces": [{"patternId": "A", "rotation": 90, "x": 2, "y": 6}, {"patternId": "5", "rotation": 180, "x": 2, "y": 5}, {"patternId": "C", "rotation": 90, "x": 2, "y": 4}, {"patternId": "E", "rotation": 0, "x": 2, "y": 3}, {"patternId": "B", "rotation": 90, "x": 1, "y": 3}, {"patternId": "A", "rotation": 180, "x": 1, "y": 2}, {"patternId": "E", "rotation": 90, "x": 2, "y": 2}, {"patternId": "A", "rotation": 180, "x": 1, "y": 2}, {"patternId": "X", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["BACK", "TOP", "FRONT", "LEFT", "BOTTOM", "FRONT", "BOTTOM", "RIGHT"], "required_slots": ["BACK", "TOP", "FRONT", "LEFT", "BOTTOM", "RIGHT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "C", "rotation": 90}, "BOTTOM": {"patternId": "A", "rotation": 90}, "FRONT": {"patternId": "E", "rotation": 0}, "BACK": {"patternId": "5", "rotation": 180}, "LEFT": {"patternId": "B", "rotation": 180}, "RIGHT": {"patternId": "X", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "C", "rotation": 90}, "BOTTOM": {"patternId": "A", "rotation": 90}, "FRONT": {"patternId": "E", "rotation": 0}, "BACK": {"patternId": "5", "rotation": 180}, "LEFT": {"patternId": "B", "rotation": 180}, "RIGHT": {"patternId": "X", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C381\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> N -> W -> N -> E -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=5, rotation=180, flipVertical=true\n- step 2: patternId=C, rotation=90, flipVertical=true\n- step 3: patternId=E, rotation=0, flipVertical=true\n- step 4: patternId=B, rotation=90, flipVertical=true\n- step 5: patternId=A, rotation=180, flipVertical=true\n- step 6: patternId=E, rotation=90, flipVertical=true\n- step 7: patternId=A, rotation=180, flipVertical=true\n- step 8: patternId=X, rotation=270, flipVertical=true\n- allowed patternId values for this task: 5, C, E, B, A, X, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C381"} +{"sample_id": "C382", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> E -> S -> W -> S -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "E", "S", "W", "S", "E", "E"], "observed_path_faces": [{"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C382_path_sequence.png"}, "metadata": {"level_id": 382, "name": "Reconstruct 382", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-382.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Y", "X", "8", "triangle", "heart", "T"], "start_x": 2, "start_y": 1, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "Y", "rotation": 180}, "BOTTOM": {"patternId": "T", "rotation": 270}, "FRONT": {"patternId": "X", "rotation": 270}, "BACK": {"patternId": "triangle", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 0}, "RIGHT": {"patternId": "8", "rotation": 90}}, "bottom_faces": [{"patternId": "T", "rotation": 270, "x": 2, "y": 1}, {"patternId": "heart", "rotation": 270, "x": 1, "y": 1}, {"patternId": "X", "rotation": 180, "x": 1, "y": 2}, {"patternId": "T", "rotation": 180, "x": 2, "y": 2}, {"patternId": "8", "rotation": 90, "x": 2, "y": 3}, {"patternId": "X", "rotation": 270, "x": 1, "y": 3}, {"patternId": "Y", "rotation": 180, "x": 1, "y": 4}, {"patternId": "8", "rotation": 0, "x": 2, "y": 4}, {"patternId": "T", "rotation": 90, "x": 3, "y": 4}], "slot_sequence": ["LEFT", "FRONT", "BOTTOM", "RIGHT", "FRONT", "TOP", "RIGHT", "BOTTOM"], "required_slots": ["LEFT", "FRONT", "BOTTOM", "RIGHT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "Y", "rotation": 180}, "BOTTOM": {"patternId": "T", "rotation": 270}, "FRONT": {"patternId": "X", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 90}, "RIGHT": {"patternId": "8", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "Y", "rotation": 180}, "BOTTOM": {"patternId": "T", "rotation": 270}, "FRONT": {"patternId": "X", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 90}, "RIGHT": {"patternId": "8", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C382\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> E -> S -> W -> S -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=heart, rotation=270, flipVertical=true\n- step 2: patternId=X, rotation=180, flipVertical=true\n- step 3: patternId=T, rotation=180, flipVertical=true\n- step 4: patternId=8, rotation=90, flipVertical=true\n- step 5: patternId=X, rotation=270, flipVertical=true\n- step 6: patternId=Y, rotation=180, flipVertical=true\n- step 7: patternId=8, rotation=0, flipVertical=true\n- step 8: patternId=T, rotation=90, flipVertical=true\n- allowed patternId values for this task: heart, X, T, 8, Y, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C382"} +{"sample_id": "C383", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> S -> W -> N -> W -> N -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "S", "W", "N", "W", "N", "S", "W"], "observed_path_faces": [{"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C383_path_sequence.png"}, "metadata": {"level_id": 383, "name": "Reconstruct 383", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-383.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["star", "J", "R", "Z", "N", "V"], "start_x": 3, "start_y": 1, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "star", "rotation": 0}, "BOTTOM": {"patternId": "V", "rotation": 270}, "FRONT": {"patternId": "J", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "N", "rotation": 180}, "RIGHT": {"patternId": "R", "rotation": 90}}, "bottom_faces": [{"patternId": "V", "rotation": 270, "x": 3, "y": 1}, {"patternId": "J", "rotation": 180, "x": 3, "y": 2}, {"patternId": "R", "rotation": 90, "x": 4, "y": 2}, {"patternId": "star", "rotation": 90, "x": 4, "y": 3}, {"patternId": "J", "rotation": 270, "x": 3, "y": 3}, {"patternId": "R", "rotation": 180, "x": 3, "y": 2}, {"patternId": "V", "rotation": 270, "x": 2, "y": 2}, {"patternId": "Z", "rotation": 270, "x": 2, "y": 1}, {"patternId": "V", "rotation": 270, "x": 2, "y": 2}, {"patternId": "N", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["FRONT", "RIGHT", "TOP", "FRONT", "RIGHT", "BOTTOM", "BACK", "BOTTOM", "LEFT"], "required_slots": ["FRONT", "RIGHT", "TOP", "BOTTOM", "BACK", "LEFT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "star", "rotation": 0}, "BOTTOM": {"patternId": "V", "rotation": 270}, "FRONT": {"patternId": "J", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "N", "rotation": 270}, "RIGHT": {"patternId": "R", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 0}, "BOTTOM": {"patternId": "V", "rotation": 270}, "FRONT": {"patternId": "J", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "N", "rotation": 270}, "RIGHT": {"patternId": "R", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C383\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> S -> W -> N -> W -> N -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=J, rotation=180, flipVertical=true\n- step 2: patternId=R, rotation=90, flipVertical=true\n- step 3: patternId=star, rotation=90, flipVertical=true\n- step 4: patternId=J, rotation=270, flipVertical=true\n- step 5: patternId=R, rotation=180, flipVertical=true\n- step 6: patternId=V, rotation=270, flipVertical=true\n- step 7: patternId=Z, rotation=270, flipVertical=true\n- step 8: patternId=V, rotation=270, flipVertical=true\n- step 9: patternId=N, rotation=90, flipVertical=true\n- allowed patternId values for this task: J, R, star, V, Z, N, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C383"} +{"sample_id": "C384", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> E -> N -> W -> S -> W -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "E", "N", "W", "S", "W", "S", "E"], "observed_path_faces": [{"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C384_path_sequence.png"}, "metadata": {"level_id": 384, "name": "Reconstruct 384", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-384.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Y", "K", "P", "J", "R", "arrow_left"], "start_x": 1, "start_y": 2, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "Y", "rotation": 0}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "K", "rotation": 180}, "BACK": {"patternId": "J", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 90}, "RIGHT": {"patternId": "P", "rotation": 0}}, "bottom_faces": [{"patternId": "arrow_left", "rotation": 0, "x": 1, "y": 2}, {"patternId": "P", "rotation": 90, "x": 2, "y": 2}, {"patternId": "Y", "rotation": 180, "x": 3, "y": 2}, {"patternId": "R", "rotation": 0, "x": 4, "y": 2}, {"patternId": "J", "rotation": 270, "x": 4, "y": 1}, {"patternId": "Y", "rotation": 90, "x": 3, "y": 1}, {"patternId": "R", "rotation": 270, "x": 3, "y": 2}, {"patternId": "K", "rotation": 0, "x": 2, "y": 2}, {"patternId": "arrow_left", "rotation": 180, "x": 2, "y": 3}, {"patternId": "R", "rotation": 180, "x": 3, "y": 3}], "slot_sequence": ["RIGHT", "TOP", "LEFT", "BACK", "TOP", "LEFT", "FRONT", "BOTTOM", "LEFT"], "required_slots": ["RIGHT", "TOP", "LEFT", "BACK", "FRONT", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "Y", "rotation": 0}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "K", "rotation": 180}, "BACK": {"patternId": "J", "rotation": 180}, "LEFT": {"patternId": "R", "rotation": 180}, "RIGHT": {"patternId": "P", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "Y", "rotation": 0}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "K", "rotation": 180}, "BACK": {"patternId": "J", "rotation": 180}, "LEFT": {"patternId": "R", "rotation": 180}, "RIGHT": {"patternId": "P", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C384\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> E -> N -> W -> S -> W -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=P, rotation=90, flipVertical=true\n- step 2: patternId=Y, rotation=180, flipVertical=true\n- step 3: patternId=R, rotation=0, flipVertical=true\n- step 4: patternId=J, rotation=270, flipVertical=true\n- step 5: patternId=Y, rotation=90, flipVertical=true\n- step 6: patternId=R, rotation=270, flipVertical=true\n- step 7: patternId=K, rotation=0, flipVertical=true\n- step 8: patternId=arrow_left, rotation=180, flipVertical=true\n- step 9: patternId=R, rotation=180, flipVertical=true\n- allowed patternId values for this task: P, Y, R, J, K, arrow_left, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C384"} +{"sample_id": "C385", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> W -> N -> N -> W -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "W", "N", "N", "W", "N", "W"], "observed_path_faces": [{"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C385_path_sequence.png"}, "metadata": {"level_id": 385, "name": "Reconstruct 385", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-385.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["W", "square", "R", "1", "7", "K"], "start_x": 5, "start_y": 3, "grid_width": 7, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "W", "rotation": 0}, "BOTTOM": {"patternId": "K", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 270}, "BACK": {"patternId": "1", "rotation": 0}, "LEFT": {"patternId": "7", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 180}}, "bottom_faces": [{"patternId": "K", "rotation": 0, "x": 5, "y": 3}, {"patternId": "7", "rotation": 270, "x": 4, "y": 3}, {"patternId": "square", "rotation": 180, "x": 4, "y": 4}, {"patternId": "W", "rotation": 270, "x": 3, "y": 4}, {"patternId": "7", "rotation": 0, "x": 3, "y": 3}, {"patternId": "K", "rotation": 90, "x": 3, "y": 2}, {"patternId": "1", "rotation": 270, "x": 2, "y": 2}, {"patternId": "R", "rotation": 90, "x": 2, "y": 1}, {"patternId": "W", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "FRONT", "TOP", "LEFT", "BOTTOM", "BACK", "RIGHT", "TOP"], "required_slots": ["LEFT", "FRONT", "TOP", "BOTTOM", "BACK", "RIGHT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "W", "rotation": 0}, "BOTTOM": {"patternId": "K", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 270}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "7", "rotation": 90}, "RIGHT": {"patternId": "R", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "W", "rotation": 0}, "BOTTOM": {"patternId": "K", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 270}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "7", "rotation": 90}, "RIGHT": {"patternId": "R", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C385\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> W -> N -> N -> W -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=7, rotation=270, flipVertical=true\n- step 2: patternId=square, rotation=180, flipVertical=true\n- step 3: patternId=W, rotation=270, flipVertical=true\n- step 4: patternId=7, rotation=0, flipVertical=true\n- step 5: patternId=K, rotation=90, flipVertical=true\n- step 6: patternId=1, rotation=270, flipVertical=true\n- step 7: patternId=R, rotation=90, flipVertical=true\n- step 8: patternId=W, rotation=0, flipVertical=true\n- allowed patternId values for this task: 7, square, W, K, 1, R, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C385"} +{"sample_id": "C386", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> W -> N -> N -> N -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "W", "N", "N", "N", "S", "E"], "observed_path_faces": [{"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C386_path_sequence.png"}, "metadata": {"level_id": 386, "name": "Reconstruct 386", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-386.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["E", "5", "1", "J", "U", "7"], "start_x": 1, "start_y": 5, "grid_width": 4, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "E", "rotation": 180}, "BOTTOM": {"patternId": "7", "rotation": 0}, "FRONT": {"patternId": "5", "rotation": 90}, "BACK": {"patternId": "J", "rotation": 90}, "LEFT": {"patternId": "U", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 90}}, "bottom_faces": [{"patternId": "7", "rotation": 0, "x": 1, "y": 5}, {"patternId": "1", "rotation": 180, "x": 2, "y": 5}, {"patternId": "J", "rotation": 180, "x": 2, "y": 4}, {"patternId": "7", "rotation": 270, "x": 1, "y": 4}, {"patternId": "U", "rotation": 180, "x": 1, "y": 3}, {"patternId": "E", "rotation": 270, "x": 1, "y": 2}, {"patternId": "1", "rotation": 90, "x": 1, "y": 1}, {"patternId": "E", "rotation": 270, "x": 1, "y": 2}, {"patternId": "J", "rotation": 0, "x": 2, "y": 2}], "slot_sequence": ["RIGHT", "BACK", "BOTTOM", "LEFT", "TOP", "RIGHT", "TOP", "BACK"], "required_slots": ["RIGHT", "BACK", "BOTTOM", "LEFT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "E", "rotation": 180}, "BOTTOM": {"patternId": "7", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "J", "rotation": 270}, "LEFT": {"patternId": "U", "rotation": 90}, "RIGHT": {"patternId": "1", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "E", "rotation": 180}, "BOTTOM": {"patternId": "7", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "J", "rotation": 270}, "LEFT": {"patternId": "U", "rotation": 90}, "RIGHT": {"patternId": "1", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C386\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> W -> N -> N -> N -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=1, rotation=180, flipVertical=true\n- step 2: patternId=J, rotation=180, flipVertical=true\n- step 3: patternId=7, rotation=270, flipVertical=true\n- step 4: patternId=U, rotation=180, flipVertical=true\n- step 5: patternId=E, rotation=270, flipVertical=true\n- step 6: patternId=1, rotation=90, flipVertical=true\n- step 7: patternId=E, rotation=270, flipVertical=true\n- step 8: patternId=J, rotation=0, flipVertical=true\n- allowed patternId values for this task: 1, J, 7, U, E, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C386"} +{"sample_id": "C387", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> W -> N -> N -> W -> N -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "W", "N", "N", "W", "N", "E", "E"], "observed_path_faces": [{"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C387_path_sequence.png"}, "metadata": {"level_id": 387, "name": "Reconstruct 387", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-387.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["I", "A", "Z", "7", "M", "F"], "start_x": 2, "start_y": 5, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "I", "rotation": 180}, "BOTTOM": {"patternId": "F", "rotation": 270}, "FRONT": {"patternId": "A", "rotation": 90}, "BACK": {"patternId": "7", "rotation": 270}, "LEFT": {"patternId": "M", "rotation": 270}, "RIGHT": {"patternId": "Z", "rotation": 270}}, "bottom_faces": [{"patternId": "F", "rotation": 270, "x": 2, "y": 5}, {"patternId": "7", "rotation": 90, "x": 2, "y": 4}, {"patternId": "Z", "rotation": 90, "x": 3, "y": 4}, {"patternId": "7", "rotation": 90, "x": 2, "y": 4}, {"patternId": "I", "rotation": 180, "x": 2, "y": 3}, {"patternId": "A", "rotation": 90, "x": 2, "y": 2}, {"patternId": "M", "rotation": 270, "x": 1, "y": 2}, {"patternId": "F", "rotation": 0, "x": 1, "y": 1}, {"patternId": "A", "rotation": 180, "x": 2, "y": 1}, {"patternId": "I", "rotation": 270, "x": 3, "y": 1}], "slot_sequence": ["BACK", "RIGHT", "BACK", "TOP", "FRONT", "LEFT", "BOTTOM", "FRONT", "TOP"], "required_slots": ["BACK", "RIGHT", "TOP", "FRONT", "LEFT", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "I", "rotation": 180}, "BOTTOM": {"patternId": "F", "rotation": 270}, "FRONT": {"patternId": "A", "rotation": 90}, "BACK": {"patternId": "7", "rotation": 90}, "LEFT": {"patternId": "M", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 180}, "BOTTOM": {"patternId": "F", "rotation": 270}, "FRONT": {"patternId": "A", "rotation": 90}, "BACK": {"patternId": "7", "rotation": 90}, "LEFT": {"patternId": "M", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C387\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> W -> N -> N -> W -> N -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=7, rotation=90, flipVertical=true\n- step 2: patternId=Z, rotation=90, flipVertical=true\n- step 3: patternId=7, rotation=90, flipVertical=true\n- step 4: patternId=I, rotation=180, flipVertical=true\n- step 5: patternId=A, rotation=90, flipVertical=true\n- step 6: patternId=M, rotation=270, flipVertical=true\n- step 7: patternId=F, rotation=0, flipVertical=true\n- step 8: patternId=A, rotation=180, flipVertical=true\n- step 9: patternId=I, rotation=270, flipVertical=true\n- allowed patternId values for this task: 7, Z, I, A, M, F, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C387"} +{"sample_id": "C388", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> E -> N -> W -> W -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "E", "N", "W", "W", "S", "S"], "observed_path_faces": [{"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C388_path_sequence.png"}, "metadata": {"level_id": 388, "name": "Reconstruct 388", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-388.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["G", "D", "arrow_right", "V", "H", "square"], "start_x": 3, "start_y": 3, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "G", "rotation": 180}, "BOTTOM": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "D", "rotation": 0}, "BACK": {"patternId": "V", "rotation": 180}, "LEFT": {"patternId": "H", "rotation": 270}, "RIGHT": {"patternId": "arrow_right", "rotation": 90}}, "bottom_faces": [{"patternId": "square", "rotation": 90, "x": 3, "y": 3}, {"patternId": "H", "rotation": 180, "x": 2, "y": 3}, {"patternId": "V", "rotation": 90, "x": 2, "y": 2}, {"patternId": "square", "rotation": 180, "x": 3, "y": 2}, {"patternId": "arrow_right", "rotation": 270, "x": 3, "y": 1}, {"patternId": "V", "rotation": 0, "x": 2, "y": 1}, {"patternId": "H", "rotation": 90, "x": 1, "y": 1}, {"patternId": "square", "rotation": 0, "x": 1, "y": 2}, {"patternId": "arrow_right", "rotation": 90, "x": 1, "y": 3}], "slot_sequence": ["LEFT", "BACK", "BOTTOM", "RIGHT", "BACK", "LEFT", "BOTTOM", "RIGHT"], "required_slots": ["LEFT", "BACK", "BOTTOM", "RIGHT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "V", "rotation": 0}, "LEFT": {"patternId": "H", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "V", "rotation": 0}, "LEFT": {"patternId": "H", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C388\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> E -> N -> W -> W -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=H, rotation=180, flipVertical=true\n- step 2: patternId=V, rotation=90, flipVertical=true\n- step 3: patternId=square, rotation=180, flipVertical=true\n- step 4: patternId=arrow_right, rotation=270, flipVertical=true\n- step 5: patternId=V, rotation=0, flipVertical=true\n- step 6: patternId=H, rotation=90, flipVertical=true\n- step 7: patternId=square, rotation=0, flipVertical=true\n- step 8: patternId=arrow_right, rotation=90, flipVertical=true\n- allowed patternId values for this task: H, V, square, arrow_right, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C388"} +{"sample_id": "C389", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> N -> N -> E -> N -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "N", "N", "E", "N", "W", "W"], "observed_path_faces": [{"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C389_path_sequence.png"}, "metadata": {"level_id": 389, "name": "Reconstruct 389", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-389.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["G", "arrow_right", "I", "I", "6", "arrow_left"], "start_x": 2, "start_y": 2, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "G", "rotation": 180}, "BOTTOM": {"patternId": "arrow_left", "rotation": 90}, "FRONT": {"patternId": "arrow_right", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 90}, "LEFT": {"patternId": "6", "rotation": 270}, "RIGHT": {"patternId": "I", "rotation": 0}}, "bottom_faces": [{"patternId": "arrow_left", "rotation": 90, "x": 2, "y": 2}, {"patternId": "arrow_right", "rotation": 0, "x": 2, "y": 3}, {"patternId": "G", "rotation": 180, "x": 2, "y": 4}, {"patternId": "arrow_right", "rotation": 0, "x": 2, "y": 3}, {"patternId": "arrow_left", "rotation": 90, "x": 2, "y": 2}, {"patternId": "I", "rotation": 90, "x": 3, "y": 2}, {"patternId": "I", "rotation": 180, "x": 3, "y": 1}, {"patternId": "arrow_left", "rotation": 0, "x": 2, "y": 1}, {"patternId": "arrow_right", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["FRONT", "TOP", "FRONT", "BOTTOM", "RIGHT", "BACK", "BOTTOM", "FRONT"], "required_slots": ["FRONT", "TOP", "BOTTOM", "RIGHT", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "G", "rotation": 180}, "BOTTOM": {"patternId": "arrow_left", "rotation": 90}, "FRONT": {"patternId": "arrow_right", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "G", "rotation": 180}, "BOTTOM": {"patternId": "arrow_left", "rotation": 90}, "FRONT": {"patternId": "arrow_right", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C389\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> N -> N -> E -> N -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_right, rotation=0, flipVertical=true\n- step 2: patternId=G, rotation=180, flipVertical=true\n- step 3: patternId=arrow_right, rotation=0, flipVertical=true\n- step 4: patternId=arrow_left, rotation=90, flipVertical=true\n- step 5: patternId=I, rotation=90, flipVertical=true\n- step 6: patternId=I, rotation=180, flipVertical=true\n- step 7: patternId=arrow_left, rotation=0, flipVertical=true\n- step 8: patternId=arrow_right, rotation=270, flipVertical=true\n- allowed patternId values for this task: arrow_right, G, arrow_left, I, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C389"} +{"sample_id": "C390", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> S -> W -> E -> W -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "S", "W", "E", "W", "W", "N"], "observed_path_faces": [{"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C390_path_sequence.png"}, "metadata": {"level_id": 390, "name": "Reconstruct 390", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-390.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["circle", "7", "L", "T", "C", "7"], "start_x": 4, "start_y": 2, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "circle", "rotation": 0}, "BOTTOM": {"patternId": "7", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 90}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "C", "rotation": 0}, "RIGHT": {"patternId": "L", "rotation": 0}}, "bottom_faces": [{"patternId": "7", "rotation": 0, "x": 4, "y": 2}, {"patternId": "T", "rotation": 0, "x": 4, "y": 1}, {"patternId": "C", "rotation": 180, "x": 3, "y": 1}, {"patternId": "7", "rotation": 270, "x": 3, "y": 2}, {"patternId": "7", "rotation": 0, "x": 2, "y": 2}, {"patternId": "7", "rotation": 270, "x": 3, "y": 2}, {"patternId": "7", "rotation": 0, "x": 2, "y": 2}, {"patternId": "circle", "rotation": 270, "x": 1, "y": 2}, {"patternId": "C", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["BACK", "LEFT", "BOTTOM", "FRONT", "BOTTOM", "FRONT", "TOP", "LEFT"], "required_slots": ["BACK", "LEFT", "BOTTOM", "FRONT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "circle", "rotation": 0}, "BOTTOM": {"patternId": "7", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 90}, "BACK": {"patternId": "T", "rotation": 0}, "LEFT": {"patternId": "C", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 0}, "BOTTOM": {"patternId": "7", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 90}, "BACK": {"patternId": "T", "rotation": 0}, "LEFT": {"patternId": "C", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C390\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> S -> W -> E -> W -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=T, rotation=0, flipVertical=true\n- step 2: patternId=C, rotation=180, flipVertical=true\n- step 3: patternId=7, rotation=270, flipVertical=true\n- step 4: patternId=7, rotation=0, flipVertical=true\n- step 5: patternId=7, rotation=270, flipVertical=true\n- step 6: patternId=7, rotation=0, flipVertical=true\n- step 7: patternId=circle, rotation=270, flipVertical=true\n- step 8: patternId=C, rotation=0, flipVertical=true\n- allowed patternId values for this task: T, C, 7, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C390"} +{"sample_id": "C391", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> S -> W -> S -> W -> S -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "S", "W", "S", "W", "S", "W", "N"], "observed_path_faces": [{"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C391_path_sequence.png"}, "metadata": {"level_id": 391, "name": "Reconstruct 391", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-391.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["X", "7", "triangle", "G", "heart", "B"], "start_x": 3, "start_y": 1, "grid_width": 6, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "X", "rotation": 90}, "BOTTOM": {"patternId": "B", "rotation": 90}, "FRONT": {"patternId": "7", "rotation": 180}, "BACK": {"patternId": "G", "rotation": 270}, "LEFT": {"patternId": "heart", "rotation": 0}, "RIGHT": {"patternId": "triangle", "rotation": 270}}, "bottom_faces": [{"patternId": "B", "rotation": 90, "x": 3, "y": 1}, {"patternId": "7", "rotation": 180, "x": 3, "y": 2}, {"patternId": "triangle", "rotation": 270, "x": 4, "y": 2}, {"patternId": "X", "rotation": 180, "x": 4, "y": 3}, {"patternId": "7", "rotation": 270, "x": 3, "y": 3}, {"patternId": "heart", "rotation": 90, "x": 3, "y": 4}, {"patternId": "B", "rotation": 270, "x": 2, "y": 4}, {"patternId": "G", "rotation": 270, "x": 2, "y": 5}, {"patternId": "triangle", "rotation": 270, "x": 1, "y": 5}, {"patternId": "B", "rotation": 0, "x": 1, "y": 4}], "slot_sequence": ["FRONT", "RIGHT", "TOP", "FRONT", "LEFT", "BOTTOM", "BACK", "RIGHT", "BOTTOM"], "required_slots": ["FRONT", "RIGHT", "TOP", "LEFT", "BOTTOM", "BACK"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "X", "rotation": 90}, "BOTTOM": {"patternId": "B", "rotation": 90}, "FRONT": {"patternId": "7", "rotation": 180}, "BACK": {"patternId": "G", "rotation": 90}, "LEFT": {"patternId": "heart", "rotation": 90}, "RIGHT": {"patternId": "triangle", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "X", "rotation": 90}, "BOTTOM": {"patternId": "B", "rotation": 90}, "FRONT": {"patternId": "7", "rotation": 180}, "BACK": {"patternId": "G", "rotation": 90}, "LEFT": {"patternId": "heart", "rotation": 90}, "RIGHT": {"patternId": "triangle", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C391\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> S -> W -> S -> W -> S -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=7, rotation=180, flipVertical=true\n- step 2: patternId=triangle, rotation=270, flipVertical=true\n- step 3: patternId=X, rotation=180, flipVertical=true\n- step 4: patternId=7, rotation=270, flipVertical=true\n- step 5: patternId=heart, rotation=90, flipVertical=true\n- step 6: patternId=B, rotation=270, flipVertical=true\n- step 7: patternId=G, rotation=270, flipVertical=true\n- step 8: patternId=triangle, rotation=270, flipVertical=true\n- step 9: patternId=B, rotation=0, flipVertical=true\n- allowed patternId values for this task: 7, triangle, X, heart, B, G, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C391"} +{"sample_id": "C392", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> E -> E -> N -> W -> W -> N -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "E", "E", "N", "W", "W", "N", "S"], "observed_path_faces": [{"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C392_path_sequence.png"}, "metadata": {"level_id": 392, "name": "Reconstruct 392", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-392.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_left", "diamond", "Y", "arrow_down", "V", "O"], "start_x": 2, "start_y": 3, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "arrow_left", "rotation": 0}, "BOTTOM": {"patternId": "O", "rotation": 270}, "FRONT": {"patternId": "diamond", "rotation": 180}, "BACK": {"patternId": "arrow_down", "rotation": 90}, "LEFT": {"patternId": "V", "rotation": 90}, "RIGHT": {"patternId": "Y", "rotation": 270}}, "bottom_faces": [{"patternId": "O", "rotation": 270, "x": 2, "y": 3}, {"patternId": "V", "rotation": 0, "x": 1, "y": 3}, {"patternId": "O", "rotation": 270, "x": 2, "y": 3}, {"patternId": "Y", "rotation": 0, "x": 3, "y": 3}, {"patternId": "arrow_down", "rotation": 180, "x": 3, "y": 2}, {"patternId": "O", "rotation": 180, "x": 2, "y": 2}, {"patternId": "diamond", "rotation": 90, "x": 1, "y": 2}, {"patternId": "V", "rotation": 0, "x": 1, "y": 1}, {"patternId": "diamond", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["LEFT", "BOTTOM", "RIGHT", "BACK", "BOTTOM", "FRONT", "LEFT", "FRONT"], "required_slots": ["LEFT", "BOTTOM", "RIGHT", "BACK", "FRONT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "O", "rotation": 270}, "FRONT": {"patternId": "diamond", "rotation": 180}, "BACK": {"patternId": "arrow_down", "rotation": 270}, "LEFT": {"patternId": "V", "rotation": 180}, "RIGHT": {"patternId": "Y", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "O", "rotation": 270}, "FRONT": {"patternId": "diamond", "rotation": 180}, "BACK": {"patternId": "arrow_down", "rotation": 270}, "LEFT": {"patternId": "V", "rotation": 180}, "RIGHT": {"patternId": "Y", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C392\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): W -> E -> E -> N -> W -> W -> N -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=V, rotation=0, flipVertical=true\n- step 2: patternId=O, rotation=270, flipVertical=true\n- step 3: patternId=Y, rotation=0, flipVertical=true\n- step 4: patternId=arrow_down, rotation=180, flipVertical=true\n- step 5: patternId=O, rotation=180, flipVertical=true\n- step 6: patternId=diamond, rotation=90, flipVertical=true\n- step 7: patternId=V, rotation=0, flipVertical=true\n- step 8: patternId=diamond, rotation=90, flipVertical=true\n- allowed patternId values for this task: V, O, Y, arrow_down, diamond, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C392"} +{"sample_id": "C393", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> S -> S -> E -> S -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "S", "S", "E", "S", "N", "W"], "observed_path_faces": [{"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C393_path_sequence.png"}, "metadata": {"level_id": 393, "name": "Reconstruct 393", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-393.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["6", "triangle", "D", "S", "C", "4"], "start_x": 2, "start_y": 1, "grid_width": 4, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "6", "rotation": 180}, "BOTTOM": {"patternId": "4", "rotation": 90}, "FRONT": {"patternId": "triangle", "rotation": 90}, "BACK": {"patternId": "S", "rotation": 180}, "LEFT": {"patternId": "C", "rotation": 270}, "RIGHT": {"patternId": "D", "rotation": 90}}, "bottom_faces": [{"patternId": "4", "rotation": 90, "x": 2, "y": 1}, {"patternId": "C", "rotation": 180, "x": 1, "y": 1}, {"patternId": "triangle", "rotation": 0, "x": 1, "y": 2}, {"patternId": "D", "rotation": 0, "x": 1, "y": 3}, {"patternId": "S", "rotation": 90, "x": 1, "y": 4}, {"patternId": "4", "rotation": 180, "x": 2, "y": 4}, {"patternId": "C", "rotation": 270, "x": 2, "y": 5}, {"patternId": "4", "rotation": 180, "x": 2, "y": 4}, {"patternId": "S", "rotation": 90, "x": 1, "y": 4}], "slot_sequence": ["LEFT", "FRONT", "RIGHT", "BACK", "BOTTOM", "LEFT", "BOTTOM", "BACK"], "required_slots": ["LEFT", "FRONT", "RIGHT", "BACK", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "4", "rotation": 90}, "FRONT": {"patternId": "triangle", "rotation": 90}, "BACK": {"patternId": "S", "rotation": 0}, "LEFT": {"patternId": "C", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "4", "rotation": 90}, "FRONT": {"patternId": "triangle", "rotation": 90}, "BACK": {"patternId": "S", "rotation": 0}, "LEFT": {"patternId": "C", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C393\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> S -> S -> E -> S -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=C, rotation=180, flipVertical=true\n- step 2: patternId=triangle, rotation=0, flipVertical=true\n- step 3: patternId=D, rotation=0, flipVertical=true\n- step 4: patternId=S, rotation=90, flipVertical=true\n- step 5: patternId=4, rotation=180, flipVertical=true\n- step 6: patternId=C, rotation=270, flipVertical=true\n- step 7: patternId=4, rotation=180, flipVertical=true\n- step 8: patternId=S, rotation=90, flipVertical=true\n- allowed patternId values for this task: C, triangle, D, S, 4, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C393"} +{"sample_id": "C394", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> W -> N -> W -> E -> E -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "W", "N", "W", "E", "E", "W"], "observed_path_faces": [{"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C394_path_sequence.png"}, "metadata": {"level_id": 394, "name": "Reconstruct 394", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-394.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["G", "X", "J", "2", "W", "arrow_up"], "start_x": 4, "start_y": 1, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "G", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "X", "rotation": 180}, "BACK": {"patternId": "2", "rotation": 180}, "LEFT": {"patternId": "W", "rotation": 270}, "RIGHT": {"patternId": "J", "rotation": 90}}, "bottom_faces": [{"patternId": "arrow_up", "rotation": 270, "x": 4, "y": 1}, {"patternId": "X", "rotation": 180, "x": 4, "y": 2}, {"patternId": "W", "rotation": 270, "x": 3, "y": 2}, {"patternId": "2", "rotation": 180, "x": 2, "y": 2}, {"patternId": "arrow_up", "rotation": 90, "x": 2, "y": 1}, {"patternId": "J", "rotation": 0, "x": 1, "y": 1}, {"patternId": "arrow_up", "rotation": 90, "x": 2, "y": 1}, {"patternId": "W", "rotation": 0, "x": 3, "y": 1}, {"patternId": "arrow_up", "rotation": 90, "x": 2, "y": 1}], "slot_sequence": ["FRONT", "LEFT", "BACK", "BOTTOM", "RIGHT", "BOTTOM", "LEFT", "BOTTOM"], "required_slots": ["FRONT", "LEFT", "BACK", "BOTTOM", "RIGHT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "X", "rotation": 180}, "BACK": {"patternId": "2", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 0}, "RIGHT": {"patternId": "J", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "X", "rotation": 180}, "BACK": {"patternId": "2", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 0}, "RIGHT": {"patternId": "J", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C394\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> W -> N -> W -> E -> E -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=X, rotation=180, flipVertical=true\n- step 2: patternId=W, rotation=270, flipVertical=true\n- step 3: patternId=2, rotation=180, flipVertical=true\n- step 4: patternId=arrow_up, rotation=90, flipVertical=true\n- step 5: patternId=J, rotation=0, flipVertical=true\n- step 6: patternId=arrow_up, rotation=90, flipVertical=true\n- step 7: patternId=W, rotation=0, flipVertical=true\n- step 8: patternId=arrow_up, rotation=90, flipVertical=true\n- allowed patternId values for this task: X, W, 2, arrow_up, J, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C394"} +{"sample_id": "C395", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> S -> S -> W -> W -> W -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "S", "S", "W", "W", "W", "S", "S"], "observed_path_faces": [{"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C395_path_sequence.png"}, "metadata": {"level_id": 395, "name": "Reconstruct 395", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-395.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["U", "K", "triangle", "plus", "K", "O"], "start_x": 3, "start_y": 1, "grid_width": 6, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "U", "rotation": 90}, "BOTTOM": {"patternId": "O", "rotation": 180}, "FRONT": {"patternId": "K", "rotation": 0}, "BACK": {"patternId": "plus", "rotation": 270}, "LEFT": {"patternId": "K", "rotation": 180}, "RIGHT": {"patternId": "triangle", "rotation": 270}}, "bottom_faces": [{"patternId": "O", "rotation": 180, "x": 3, "y": 1}, {"patternId": "K", "rotation": 0, "x": 3, "y": 2}, {"patternId": "triangle", "rotation": 270, "x": 4, "y": 2}, {"patternId": "U", "rotation": 180, "x": 4, "y": 3}, {"patternId": "K", "rotation": 0, "x": 4, "y": 4}, {"patternId": "K", "rotation": 180, "x": 3, "y": 4}, {"patternId": "triangle", "rotation": 90, "x": 2, "y": 4}, {"patternId": "plus", "rotation": 90, "x": 1, "y": 4}, {"patternId": "O", "rotation": 180, "x": 1, "y": 5}, {"patternId": "K", "rotation": 0, "x": 1, "y": 6}], "slot_sequence": ["FRONT", "RIGHT", "TOP", "LEFT", "FRONT", "RIGHT", "BACK", "BOTTOM", "FRONT"], "required_slots": ["FRONT", "RIGHT", "TOP", "LEFT", "BACK", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "U", "rotation": 90}, "BOTTOM": {"patternId": "O", "rotation": 180}, "FRONT": {"patternId": "K", "rotation": 0}, "BACK": {"patternId": "plus", "rotation": 90}, "LEFT": {"patternId": "K", "rotation": 270}, "RIGHT": {"patternId": "triangle", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "U", "rotation": 90}, "BOTTOM": {"patternId": "O", "rotation": 180}, "FRONT": {"patternId": "K", "rotation": 0}, "BACK": {"patternId": "plus", "rotation": 90}, "LEFT": {"patternId": "K", "rotation": 270}, "RIGHT": {"patternId": "triangle", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C395\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> S -> S -> W -> W -> W -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=K, rotation=0, flipVertical=true\n- step 2: patternId=triangle, rotation=270, flipVertical=true\n- step 3: patternId=U, rotation=180, flipVertical=true\n- step 4: patternId=K, rotation=0, flipVertical=true\n- step 5: patternId=K, rotation=180, flipVertical=true\n- step 6: patternId=triangle, rotation=90, flipVertical=true\n- step 7: patternId=plus, rotation=90, flipVertical=true\n- step 8: patternId=O, rotation=180, flipVertical=true\n- step 9: patternId=K, rotation=0, flipVertical=true\n- allowed patternId values for this task: K, triangle, U, plus, O, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C395"} +{"sample_id": "C396", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> E -> S -> W -> W -> S -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "E", "S", "W", "W", "S", "W", "N"], "observed_path_faces": [{"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C396_path_sequence.png"}, "metadata": {"level_id": 396, "name": "Reconstruct 396", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-396.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["2", "C", "K", "Z", "smile", "F"], "start_x": 2, "start_y": 2, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "2", "rotation": 180}, "BOTTOM": {"patternId": "F", "rotation": 90}, "FRONT": {"patternId": "C", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "smile", "rotation": 0}, "RIGHT": {"patternId": "K", "rotation": 90}}, "bottom_faces": [{"patternId": "F", "rotation": 90, "x": 2, "y": 2}, {"patternId": "Z", "rotation": 90, "x": 2, "y": 1}, {"patternId": "K", "rotation": 270, "x": 3, "y": 1}, {"patternId": "C", "rotation": 0, "x": 4, "y": 1}, {"patternId": "F", "rotation": 270, "x": 4, "y": 2}, {"patternId": "K", "rotation": 0, "x": 3, "y": 2}, {"patternId": "2", "rotation": 180, "x": 2, "y": 2}, {"patternId": "Z", "rotation": 90, "x": 2, "y": 3}, {"patternId": "smile", "rotation": 180, "x": 1, "y": 3}, {"patternId": "2", "rotation": 270, "x": 1, "y": 2}], "slot_sequence": ["BACK", "RIGHT", "FRONT", "BOTTOM", "RIGHT", "TOP", "BACK", "LEFT", "TOP"], "required_slots": ["BACK", "RIGHT", "FRONT", "BOTTOM", "TOP", "LEFT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "2", "rotation": 180}, "BOTTOM": {"patternId": "F", "rotation": 90}, "FRONT": {"patternId": "C", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "smile", "rotation": 90}, "RIGHT": {"patternId": "K", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "2", "rotation": 180}, "BOTTOM": {"patternId": "F", "rotation": 90}, "FRONT": {"patternId": "C", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "smile", "rotation": 90}, "RIGHT": {"patternId": "K", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C396\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> E -> S -> W -> W -> S -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Z, rotation=90, flipVertical=true\n- step 2: patternId=K, rotation=270, flipVertical=true\n- step 3: patternId=C, rotation=0, flipVertical=true\n- step 4: patternId=F, rotation=270, flipVertical=true\n- step 5: patternId=K, rotation=0, flipVertical=true\n- step 6: patternId=2, rotation=180, flipVertical=true\n- step 7: patternId=Z, rotation=90, flipVertical=true\n- step 8: patternId=smile, rotation=180, flipVertical=true\n- step 9: patternId=2, rotation=270, flipVertical=true\n- allowed patternId values for this task: Z, K, C, F, 2, smile, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C396"} +{"sample_id": "C397", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> N -> N -> S -> W -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "N", "N", "S", "W", "N", "N"], "observed_path_faces": [{"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C397_path_sequence.png"}, "metadata": {"level_id": 397, "name": "Reconstruct 397", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-397.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["D", "T", "P", "arrow_up", "C", "K"], "start_x": 1, "start_y": 4, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "D", "rotation": 270}, "BOTTOM": {"patternId": "K", "rotation": 0}, "FRONT": {"patternId": "T", "rotation": 180}, "BACK": {"patternId": "arrow_up", "rotation": 90}, "LEFT": {"patternId": "C", "rotation": 0}, "RIGHT": {"patternId": "P", "rotation": 0}}, "bottom_faces": [{"patternId": "K", "rotation": 0, "x": 1, "y": 4}, {"patternId": "P", "rotation": 90, "x": 2, "y": 4}, {"patternId": "D", "rotation": 90, "x": 3, "y": 4}, {"patternId": "arrow_up", "rotation": 90, "x": 3, "y": 3}, {"patternId": "K", "rotation": 180, "x": 3, "y": 2}, {"patternId": "arrow_up", "rotation": 90, "x": 3, "y": 3}, {"patternId": "P", "rotation": 0, "x": 2, "y": 3}, {"patternId": "K", "rotation": 270, "x": 2, "y": 2}, {"patternId": "C", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["RIGHT", "TOP", "BACK", "BOTTOM", "BACK", "RIGHT", "BOTTOM", "LEFT"], "required_slots": ["RIGHT", "TOP", "BACK", "BOTTOM", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "D", "rotation": 270}, "BOTTOM": {"patternId": "K", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_up", "rotation": 270}, "LEFT": {"patternId": "C", "rotation": 90}, "RIGHT": {"patternId": "P", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "D", "rotation": 270}, "BOTTOM": {"patternId": "K", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_up", "rotation": 270}, "LEFT": {"patternId": "C", "rotation": 90}, "RIGHT": {"patternId": "P", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C397\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> N -> N -> S -> W -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=P, rotation=90, flipVertical=true\n- step 2: patternId=D, rotation=90, flipVertical=true\n- step 3: patternId=arrow_up, rotation=90, flipVertical=true\n- step 4: patternId=K, rotation=180, flipVertical=true\n- step 5: patternId=arrow_up, rotation=90, flipVertical=true\n- step 6: patternId=P, rotation=0, flipVertical=true\n- step 7: patternId=K, rotation=270, flipVertical=true\n- step 8: patternId=C, rotation=180, flipVertical=true\n- allowed patternId values for this task: P, D, arrow_up, K, C, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C397"} +{"sample_id": "C398", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> N -> E -> N -> W -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "N", "E", "N", "W", "S", "W"], "observed_path_faces": [{"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C398_path_sequence.png"}, "metadata": {"level_id": 398, "name": "Reconstruct 398", "difficulty": 4, "move_count": 8, "tier": 4, "source_level_path": "levels/reconstruct/generated-398.json", "tier_label": "Difficulty 4"}, "description": "8-move reconstruct puzzle", "net_faces": [{"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["I", "triangle", "1", "1", "Y", "arrow_left"], "start_x": 1, "start_y": 3, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "I", "rotation": 270}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "triangle", "rotation": 180}, "BACK": {"patternId": "1", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 180}, "RIGHT": {"patternId": "1", "rotation": 0}}, "bottom_faces": [{"patternId": "arrow_left", "rotation": 0, "x": 1, "y": 3}, {"patternId": "1", "rotation": 90, "x": 2, "y": 3}, {"patternId": "I", "rotation": 90, "x": 3, "y": 3}, {"patternId": "1", "rotation": 0, "x": 3, "y": 2}, {"patternId": "Y", "rotation": 180, "x": 4, "y": 2}, {"patternId": "arrow_left", "rotation": 90, "x": 4, "y": 1}, {"patternId": "1", "rotation": 270, "x": 3, "y": 1}, {"patternId": "Y", "rotation": 90, "x": 3, "y": 2}, {"patternId": "I", "rotation": 90, "x": 2, "y": 2}], "slot_sequence": ["RIGHT", "TOP", "BACK", "LEFT", "BOTTOM", "BACK", "LEFT", "TOP"], "required_slots": ["RIGHT", "TOP", "BACK", "LEFT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "I", "rotation": 270}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "Y", "rotation": 270}, "RIGHT": {"patternId": "1", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 270}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "Y", "rotation": 270}, "RIGHT": {"patternId": "1", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C398\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> N -> E -> N -> W -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=1, rotation=90, flipVertical=true\n- step 2: patternId=I, rotation=90, flipVertical=true\n- step 3: patternId=1, rotation=0, flipVertical=true\n- step 4: patternId=Y, rotation=180, flipVertical=true\n- step 5: patternId=arrow_left, rotation=90, flipVertical=true\n- step 6: patternId=1, rotation=270, flipVertical=true\n- step 7: patternId=Y, rotation=90, flipVertical=true\n- step 8: patternId=I, rotation=90, flipVertical=true\n- allowed patternId values for this task: 1, I, Y, arrow_left, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C398"} +{"sample_id": "C399", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> W -> S -> N -> N -> E -> N -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "W", "S", "N", "N", "E", "N", "S"], "observed_path_faces": [{"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C399_path_sequence.png"}, "metadata": {"level_id": 399, "name": "Reconstruct 399", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-399.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["square", "arrow_down", "F", "R", "C", "arrow_down"], "start_x": 3, "start_y": 4, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "square", "rotation": 90}, "BOTTOM": {"patternId": "arrow_down", "rotation": 180}, "FRONT": {"patternId": "arrow_down", "rotation": 270}, "BACK": {"patternId": "R", "rotation": 270}, "LEFT": {"patternId": "C", "rotation": 90}, "RIGHT": {"patternId": "F", "rotation": 270}}, "bottom_faces": [{"patternId": "arrow_down", "rotation": 180, "x": 3, "y": 4}, {"patternId": "R", "rotation": 90, "x": 3, "y": 3}, {"patternId": "C", "rotation": 270, "x": 2, "y": 3}, {"patternId": "arrow_down", "rotation": 90, "x": 1, "y": 3}, {"patternId": "arrow_down", "rotation": 0, "x": 1, "y": 4}, {"patternId": "arrow_down", "rotation": 90, "x": 1, "y": 3}, {"patternId": "square", "rotation": 270, "x": 1, "y": 2}, {"patternId": "C", "rotation": 0, "x": 2, "y": 2}, {"patternId": "R", "rotation": 180, "x": 2, "y": 1}, {"patternId": "C", "rotation": 0, "x": 2, "y": 2}], "slot_sequence": ["BACK", "LEFT", "FRONT", "BOTTOM", "FRONT", "TOP", "LEFT", "BACK", "LEFT"], "required_slots": ["BACK", "LEFT", "FRONT", "BOTTOM", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "square", "rotation": 90}, "BOTTOM": {"patternId": "arrow_down", "rotation": 180}, "FRONT": {"patternId": "arrow_down", "rotation": 270}, "BACK": {"patternId": "R", "rotation": 90}, "LEFT": {"patternId": "C", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "square", "rotation": 90}, "BOTTOM": {"patternId": "arrow_down", "rotation": 180}, "FRONT": {"patternId": "arrow_down", "rotation": 270}, "BACK": {"patternId": "R", "rotation": 90}, "LEFT": {"patternId": "C", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C399\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> W -> S -> N -> N -> E -> N -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=R, rotation=90, flipVertical=true\n- step 2: patternId=C, rotation=270, flipVertical=true\n- step 3: patternId=arrow_down, rotation=90, flipVertical=true\n- step 4: patternId=arrow_down, rotation=0, flipVertical=true\n- step 5: patternId=arrow_down, rotation=90, flipVertical=true\n- step 6: patternId=square, rotation=270, flipVertical=true\n- step 7: patternId=C, rotation=0, flipVertical=true\n- step 8: patternId=R, rotation=180, flipVertical=true\n- step 9: patternId=C, rotation=0, flipVertical=true\n- allowed patternId values for this task: R, C, arrow_down, square, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C399"} +{"sample_id": "C400", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> E -> W -> W -> S -> N -> N -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "E", "W", "W", "S", "N", "N", "S"], "observed_path_faces": [{"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C400_path_sequence.png"}, "metadata": {"level_id": 400, "name": "Reconstruct 400", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-400.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["N", "circle", "Q", "V", "4", "G"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "N", "rotation": 180}, "BOTTOM": {"patternId": "G", "rotation": 270}, "FRONT": {"patternId": "circle", "rotation": 270}, "BACK": {"patternId": "V", "rotation": 180}, "LEFT": {"patternId": "4", "rotation": 270}, "RIGHT": {"patternId": "Q", "rotation": 90}}, "bottom_faces": [{"patternId": "G", "rotation": 270, "x": 1, "y": 1}, {"patternId": "circle", "rotation": 270, "x": 1, "y": 2}, {"patternId": "Q", "rotation": 90, "x": 2, "y": 2}, {"patternId": "V", "rotation": 180, "x": 3, "y": 2}, {"patternId": "Q", "rotation": 90, "x": 2, "y": 2}, {"patternId": "circle", "rotation": 270, "x": 1, "y": 2}, {"patternId": "N", "rotation": 180, "x": 1, "y": 3}, {"patternId": "circle", "rotation": 270, "x": 1, "y": 2}, {"patternId": "G", "rotation": 270, "x": 1, "y": 1}, {"patternId": "circle", "rotation": 270, "x": 1, "y": 2}], "slot_sequence": ["FRONT", "RIGHT", "BACK", "RIGHT", "FRONT", "TOP", "FRONT", "BOTTOM", "FRONT"], "required_slots": ["FRONT", "RIGHT", "BACK", "TOP", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "N", "rotation": 180}, "BOTTOM": {"patternId": "G", "rotation": 270}, "FRONT": {"patternId": "circle", "rotation": 270}, "BACK": {"patternId": "V", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Q", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "N", "rotation": 180}, "BOTTOM": {"patternId": "G", "rotation": 270}, "FRONT": {"patternId": "circle", "rotation": 270}, "BACK": {"patternId": "V", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Q", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C400\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> E -> W -> W -> S -> N -> N -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=circle, rotation=270, flipVertical=true\n- step 2: patternId=Q, rotation=90, flipVertical=true\n- step 3: patternId=V, rotation=180, flipVertical=true\n- step 4: patternId=Q, rotation=90, flipVertical=true\n- step 5: patternId=circle, rotation=270, flipVertical=true\n- step 6: patternId=N, rotation=180, flipVertical=true\n- step 7: patternId=circle, rotation=270, flipVertical=true\n- step 8: patternId=G, rotation=270, flipVertical=true\n- step 9: patternId=circle, rotation=270, flipVertical=true\n- allowed patternId values for this task: circle, Q, V, N, G, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C400"} +{"sample_id": "C401", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> E -> S -> W -> W -> W -> S -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "E", "S", "W", "W", "W", "S", "S", "W"], "observed_path_faces": [{"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C401_path_sequence.png"}, "metadata": {"level_id": 401, "name": "Reconstruct 401", "difficulty": 4, "move_count": 9, "tier": 4, "source_level_path": "levels/reconstruct/generated-401.json", "tier_label": "Difficulty 4"}, "description": "9-move reconstruct puzzle", "net_faces": [{"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["star", "2", "L", "F", "O", "R"], "start_x": 5, "start_y": 1, "grid_width": 7, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "star", "rotation": 180}, "BOTTOM": {"patternId": "R", "rotation": 90}, "FRONT": {"patternId": "2", "rotation": 90}, "BACK": {"patternId": "F", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 0}, "RIGHT": {"patternId": "L", "rotation": 270}}, "bottom_faces": [{"patternId": "R", "rotation": 90, "x": 5, "y": 1}, {"patternId": "O", "rotation": 270, "x": 4, "y": 1}, {"patternId": "R", "rotation": 90, "x": 5, "y": 1}, {"patternId": "2", "rotation": 90, "x": 5, "y": 2}, {"patternId": "O", "rotation": 0, "x": 4, "y": 2}, {"patternId": "F", "rotation": 0, "x": 3, "y": 2}, {"patternId": "L", "rotation": 270, "x": 2, "y": 2}, {"patternId": "star", "rotation": 270, "x": 2, "y": 3}, {"patternId": "O", "rotation": 180, "x": 2, "y": 4}, {"patternId": "2", "rotation": 270, "x": 1, "y": 4}], "slot_sequence": ["LEFT", "BOTTOM", "FRONT", "LEFT", "BACK", "RIGHT", "TOP", "LEFT", "FRONT"], "required_slots": ["LEFT", "BOTTOM", "FRONT", "BACK", "RIGHT", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "star", "rotation": 180}, "BOTTOM": {"patternId": "R", "rotation": 90}, "FRONT": {"patternId": "2", "rotation": 90}, "BACK": {"patternId": "F", "rotation": 180}, "LEFT": {"patternId": "O", "rotation": 90}, "RIGHT": {"patternId": "L", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 180}, "BOTTOM": {"patternId": "R", "rotation": 90}, "FRONT": {"patternId": "2", "rotation": 90}, "BACK": {"patternId": "F", "rotation": 180}, "LEFT": {"patternId": "O", "rotation": 90}, "RIGHT": {"patternId": "L", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C401\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): W -> E -> S -> W -> W -> W -> S -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=O, rotation=270, flipVertical=true\n- step 2: patternId=R, rotation=90, flipVertical=true\n- step 3: patternId=2, rotation=90, flipVertical=true\n- step 4: patternId=O, rotation=0, flipVertical=true\n- step 5: patternId=F, rotation=0, flipVertical=true\n- step 6: patternId=L, rotation=270, flipVertical=true\n- step 7: patternId=star, rotation=270, flipVertical=true\n- step 8: patternId=O, rotation=180, flipVertical=true\n- step 9: patternId=2, rotation=270, flipVertical=true\n- allowed patternId values for this task: O, R, 2, F, L, star, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C401"} +{"sample_id": "C402", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> N -> E -> N -> E -> W -> S -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "N", "E", "N", "E", "W", "S", "W", "S"], "observed_path_faces": [{"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C402_path_sequence.png"}, "metadata": {"level_id": 402, "name": "Reconstruct 402", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-402.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["M", "circle", "D", "7", "V", "smile"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "M", "rotation": 180}, "BOTTOM": {"patternId": "smile", "rotation": 180}, "FRONT": {"patternId": "circle", "rotation": 90}, "BACK": {"patternId": "7", "rotation": 0}, "LEFT": {"patternId": "V", "rotation": 180}, "RIGHT": {"patternId": "D", "rotation": 0}}, "bottom_faces": [{"patternId": "smile", "rotation": 180, "x": 1, "y": 1}, {"patternId": "circle", "rotation": 90, "x": 1, "y": 2}, {"patternId": "M", "rotation": 180, "x": 1, "y": 3}, {"patternId": "circle", "rotation": 90, "x": 1, "y": 2}, {"patternId": "D", "rotation": 0, "x": 2, "y": 2}, {"patternId": "smile", "rotation": 90, "x": 2, "y": 1}, {"patternId": "7", "rotation": 90, "x": 3, "y": 1}, {"patternId": "smile", "rotation": 90, "x": 2, "y": 1}, {"patternId": "D", "rotation": 0, "x": 2, "y": 2}, {"patternId": "circle", "rotation": 90, "x": 1, "y": 2}, {"patternId": "M", "rotation": 180, "x": 1, "y": 3}], "slot_sequence": ["FRONT", "TOP", "FRONT", "RIGHT", "BOTTOM", "BACK", "BOTTOM", "RIGHT", "FRONT", "TOP"], "required_slots": ["FRONT", "TOP", "RIGHT", "BOTTOM", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "M", "rotation": 180}, "BOTTOM": {"patternId": "smile", "rotation": 180}, "FRONT": {"patternId": "circle", "rotation": 90}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 180}, "BOTTOM": {"patternId": "smile", "rotation": 180}, "FRONT": {"patternId": "circle", "rotation": 90}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C402\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> N -> E -> N -> E -> W -> S -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=circle, rotation=90, flipVertical=true\n- step 2: patternId=M, rotation=180, flipVertical=true\n- step 3: patternId=circle, rotation=90, flipVertical=true\n- step 4: patternId=D, rotation=0, flipVertical=true\n- step 5: patternId=smile, rotation=90, flipVertical=true\n- step 6: patternId=7, rotation=90, flipVertical=true\n- step 7: patternId=smile, rotation=90, flipVertical=true\n- step 8: patternId=D, rotation=0, flipVertical=true\n- step 9: patternId=circle, rotation=90, flipVertical=true\n- step 10: patternId=M, rotation=180, flipVertical=true\n- allowed patternId values for this task: circle, M, D, smile, 7, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C402"} +{"sample_id": "C403", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> E -> N -> S -> S -> W -> W -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "E", "N", "S", "S", "W", "W", "N", "E"], "observed_path_faces": [{"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C403_path_sequence.png"}, "metadata": {"level_id": 403, "name": "Reconstruct 403", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-403.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["diamond", "N", "N", "triangle", "plus", "star"], "start_x": 4, "start_y": 2, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "diamond", "rotation": 270}, "BOTTOM": {"patternId": "star", "rotation": 90}, "FRONT": {"patternId": "N", "rotation": 270}, "BACK": {"patternId": "triangle", "rotation": 270}, "LEFT": {"patternId": "plus", "rotation": 270}, "RIGHT": {"patternId": "N", "rotation": 0}}, "bottom_faces": [{"patternId": "star", "rotation": 90, "x": 4, "y": 2}, {"patternId": "plus", "rotation": 180, "x": 3, "y": 2}, {"patternId": "diamond", "rotation": 90, "x": 2, "y": 2}, {"patternId": "plus", "rotation": 180, "x": 3, "y": 2}, {"patternId": "triangle", "rotation": 180, "x": 3, "y": 1}, {"patternId": "plus", "rotation": 180, "x": 3, "y": 2}, {"patternId": "N", "rotation": 180, "x": 3, "y": 3}, {"patternId": "diamond", "rotation": 180, "x": 2, "y": 3}, {"patternId": "triangle", "rotation": 0, "x": 1, "y": 3}, {"patternId": "plus", "rotation": 0, "x": 1, "y": 2}, {"patternId": "diamond", "rotation": 270, "x": 2, "y": 2}], "slot_sequence": ["LEFT", "TOP", "LEFT", "BACK", "LEFT", "FRONT", "TOP", "BACK", "LEFT", "TOP"], "required_slots": ["LEFT", "TOP", "BACK", "FRONT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "diamond", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 270}, "BACK": {"patternId": "triangle", "rotation": 90}, "LEFT": {"patternId": "plus", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "diamond", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 270}, "BACK": {"patternId": "triangle", "rotation": 90}, "LEFT": {"patternId": "plus", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C403\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> E -> N -> S -> S -> W -> W -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=plus, rotation=180, flipVertical=true\n- step 2: patternId=diamond, rotation=90, flipVertical=true\n- step 3: patternId=plus, rotation=180, flipVertical=true\n- step 4: patternId=triangle, rotation=180, flipVertical=true\n- step 5: patternId=plus, rotation=180, flipVertical=true\n- step 6: patternId=N, rotation=180, flipVertical=true\n- step 7: patternId=diamond, rotation=180, flipVertical=true\n- step 8: patternId=triangle, rotation=0, flipVertical=true\n- step 9: patternId=plus, rotation=0, flipVertical=true\n- step 10: patternId=diamond, rotation=270, flipVertical=true\n- allowed patternId values for this task: plus, diamond, triangle, N, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C403"} +{"sample_id": "C404", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> N -> W -> S -> E -> W -> S -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "N", "W", "S", "E", "W", "S", "E", "E"], "observed_path_faces": [{"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C404_path_sequence.png"}, "metadata": {"level_id": 404, "name": "Reconstruct 404", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-404.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["O", "U", "6", "9", "3", "diamond"], "start_x": 4, "start_y": 2, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "O", "rotation": 90}, "BOTTOM": {"patternId": "diamond", "rotation": 180}, "FRONT": {"patternId": "U", "rotation": 0}, "BACK": {"patternId": "9", "rotation": 180}, "LEFT": {"patternId": "3", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 180}}, "bottom_faces": [{"patternId": "diamond", "rotation": 180, "x": 4, "y": 2}, {"patternId": "3", "rotation": 270, "x": 3, "y": 2}, {"patternId": "O", "rotation": 270, "x": 2, "y": 2}, {"patternId": "9", "rotation": 180, "x": 2, "y": 1}, {"patternId": "6", "rotation": 180, "x": 1, "y": 1}, {"patternId": "O", "rotation": 180, "x": 1, "y": 2}, {"patternId": "9", "rotation": 90, "x": 2, "y": 2}, {"patternId": "O", "rotation": 180, "x": 1, "y": 2}, {"patternId": "3", "rotation": 180, "x": 1, "y": 3}, {"patternId": "9", "rotation": 0, "x": 2, "y": 3}, {"patternId": "6", "rotation": 0, "x": 3, "y": 3}], "slot_sequence": ["LEFT", "TOP", "BACK", "RIGHT", "TOP", "BACK", "TOP", "LEFT", "BACK", "RIGHT"], "required_slots": ["LEFT", "TOP", "BACK", "RIGHT"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "O", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "9", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 90}, "RIGHT": {"patternId": "6", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "9", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 90}, "RIGHT": {"patternId": "6", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C404\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> N -> W -> S -> E -> W -> S -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=3, rotation=270, flipVertical=true\n- step 2: patternId=O, rotation=270, flipVertical=true\n- step 3: patternId=9, rotation=180, flipVertical=true\n- step 4: patternId=6, rotation=180, flipVertical=true\n- step 5: patternId=O, rotation=180, flipVertical=true\n- step 6: patternId=9, rotation=90, flipVertical=true\n- step 7: patternId=O, rotation=180, flipVertical=true\n- step 8: patternId=3, rotation=180, flipVertical=true\n- step 9: patternId=9, rotation=0, flipVertical=true\n- step 10: patternId=6, rotation=0, flipVertical=true\n- allowed patternId values for this task: 3, O, 9, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C404"} +{"sample_id": "C405", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> E -> N -> E -> S -> E -> N -> W -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "E", "N", "E", "S", "E", "N", "W", "E"], "observed_path_faces": [{"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C405_path_sequence.png"}, "metadata": {"level_id": 405, "name": "Reconstruct 405", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-405.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["N", "9", "D", "plus", "L", "N"], "start_x": 1, "start_y": 1, "grid_width": 7, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "N", "rotation": 180}, "BOTTOM": {"patternId": "N", "rotation": 270}, "FRONT": {"patternId": "9", "rotation": 0}, "BACK": {"patternId": "plus", "rotation": 270}, "LEFT": {"patternId": "L", "rotation": 90}, "RIGHT": {"patternId": "D", "rotation": 90}}, "bottom_faces": [{"patternId": "N", "rotation": 270, "x": 1, "y": 1}, {"patternId": "D", "rotation": 180, "x": 2, "y": 1}, {"patternId": "9", "rotation": 90, "x": 2, "y": 2}, {"patternId": "N", "rotation": 270, "x": 3, "y": 2}, {"patternId": "D", "rotation": 90, "x": 3, "y": 1}, {"patternId": "plus", "rotation": 270, "x": 4, "y": 1}, {"patternId": "N", "rotation": 0, "x": 4, "y": 2}, {"patternId": "L", "rotation": 0, "x": 5, "y": 2}, {"patternId": "plus", "rotation": 180, "x": 5, "y": 1}, {"patternId": "N", "rotation": 270, "x": 4, "y": 1}, {"patternId": "plus", "rotation": 180, "x": 5, "y": 1}], "slot_sequence": ["RIGHT", "FRONT", "TOP", "RIGHT", "BACK", "TOP", "LEFT", "BACK", "TOP", "BACK"], "required_slots": ["RIGHT", "FRONT", "TOP", "BACK", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "N", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "9", "rotation": 0}, "BACK": {"patternId": "plus", "rotation": 90}, "LEFT": {"patternId": "L", "rotation": 180}, "RIGHT": {"patternId": "D", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "N", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "9", "rotation": 0}, "BACK": {"patternId": "plus", "rotation": 90}, "LEFT": {"patternId": "L", "rotation": 180}, "RIGHT": {"patternId": "D", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C405\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> E -> N -> E -> S -> E -> N -> W -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=D, rotation=180, flipVertical=true\n- step 2: patternId=9, rotation=90, flipVertical=true\n- step 3: patternId=N, rotation=270, flipVertical=true\n- step 4: patternId=D, rotation=90, flipVertical=true\n- step 5: patternId=plus, rotation=270, flipVertical=true\n- step 6: patternId=N, rotation=0, flipVertical=true\n- step 7: patternId=L, rotation=0, flipVertical=true\n- step 8: patternId=plus, rotation=180, flipVertical=true\n- step 9: patternId=N, rotation=270, flipVertical=true\n- step 10: patternId=plus, rotation=180, flipVertical=true\n- allowed patternId values for this task: D, 9, N, plus, L, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C405"} +{"sample_id": "C406", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> E -> S -> E -> S -> S -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "W", "E", "S", "E", "S", "S", "S", "W"], "observed_path_faces": [{"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C406_path_sequence.png"}, "metadata": {"level_id": 406, "name": "Reconstruct 406", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-406.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["P", "Y", "X", "L", "Y", "C"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "P", "rotation": 180}, "BOTTOM": {"patternId": "C", "rotation": 0}, "FRONT": {"patternId": "Y", "rotation": 0}, "BACK": {"patternId": "L", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 180}, "RIGHT": {"patternId": "X", "rotation": 90}}, "bottom_faces": [{"patternId": "C", "rotation": 0, "x": 1, "y": 1}, {"patternId": "X", "rotation": 180, "x": 2, "y": 1}, {"patternId": "Y", "rotation": 90, "x": 2, "y": 2}, {"patternId": "C", "rotation": 90, "x": 1, "y": 2}, {"patternId": "Y", "rotation": 90, "x": 2, "y": 2}, {"patternId": "Y", "rotation": 270, "x": 2, "y": 3}, {"patternId": "P", "rotation": 180, "x": 3, "y": 3}, {"patternId": "L", "rotation": 180, "x": 3, "y": 4}, {"patternId": "C", "rotation": 0, "x": 3, "y": 5}, {"patternId": "Y", "rotation": 0, "x": 3, "y": 6}, {"patternId": "Y", "rotation": 180, "x": 2, "y": 6}], "slot_sequence": ["RIGHT", "FRONT", "BOTTOM", "FRONT", "LEFT", "TOP", "BACK", "BOTTOM", "FRONT", "LEFT"], "required_slots": ["RIGHT", "FRONT", "BOTTOM", "LEFT", "TOP", "BACK"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "P", "rotation": 180}, "BOTTOM": {"patternId": "C", "rotation": 0}, "FRONT": {"patternId": "Y", "rotation": 0}, "BACK": {"patternId": "L", "rotation": 180}, "LEFT": {"patternId": "Y", "rotation": 270}, "RIGHT": {"patternId": "X", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "P", "rotation": 180}, "BOTTOM": {"patternId": "C", "rotation": 0}, "FRONT": {"patternId": "Y", "rotation": 0}, "BACK": {"patternId": "L", "rotation": 180}, "LEFT": {"patternId": "Y", "rotation": 270}, "RIGHT": {"patternId": "X", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C406\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> E -> S -> E -> S -> S -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=X, rotation=180, flipVertical=true\n- step 2: patternId=Y, rotation=90, flipVertical=true\n- step 3: patternId=C, rotation=90, flipVertical=true\n- step 4: patternId=Y, rotation=90, flipVertical=true\n- step 5: patternId=Y, rotation=270, flipVertical=true\n- step 6: patternId=P, rotation=180, flipVertical=true\n- step 7: patternId=L, rotation=180, flipVertical=true\n- step 8: patternId=C, rotation=0, flipVertical=true\n- step 9: patternId=Y, rotation=0, flipVertical=true\n- step 10: patternId=Y, rotation=180, flipVertical=true\n- allowed patternId values for this task: X, Y, C, P, L, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C406"} +{"sample_id": "C407", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> N -> S -> W -> S -> W -> S -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "N", "S", "W", "S", "W", "S", "W", "N"], "observed_path_faces": [{"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C407_path_sequence.png"}, "metadata": {"level_id": 407, "name": "Reconstruct 407", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-407.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["8", "U", "S", "B", "arrow_down", "2"], "start_x": 6, "start_y": 2, "grid_width": 8, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "8", "rotation": 0}, "BOTTOM": {"patternId": "2", "rotation": 0}, "FRONT": {"patternId": "U", "rotation": 180}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "arrow_down", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 180}}, "bottom_faces": [{"patternId": "2", "rotation": 0, "x": 6, "y": 2}, {"patternId": "arrow_down", "rotation": 270, "x": 5, "y": 2}, {"patternId": "8", "rotation": 180, "x": 4, "y": 2}, {"patternId": "B", "rotation": 0, "x": 4, "y": 1}, {"patternId": "8", "rotation": 180, "x": 4, "y": 2}, {"patternId": "S", "rotation": 270, "x": 3, "y": 2}, {"patternId": "U", "rotation": 270, "x": 3, "y": 3}, {"patternId": "2", "rotation": 90, "x": 2, "y": 3}, {"patternId": "arrow_down", "rotation": 0, "x": 2, "y": 4}, {"patternId": "B", "rotation": 0, "x": 1, "y": 4}, {"patternId": "2", "rotation": 180, "x": 1, "y": 3}], "slot_sequence": ["LEFT", "TOP", "BACK", "TOP", "RIGHT", "FRONT", "BOTTOM", "LEFT", "BACK", "BOTTOM"], "required_slots": ["LEFT", "TOP", "BACK", "RIGHT", "FRONT", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "8", "rotation": 0}, "BOTTOM": {"patternId": "2", "rotation": 0}, "FRONT": {"patternId": "U", "rotation": 180}, "BACK": {"patternId": "B", "rotation": 180}, "LEFT": {"patternId": "arrow_down", "rotation": 90}, "RIGHT": {"patternId": "S", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "8", "rotation": 0}, "BOTTOM": {"patternId": "2", "rotation": 0}, "FRONT": {"patternId": "U", "rotation": 180}, "BACK": {"patternId": "B", "rotation": 180}, "LEFT": {"patternId": "arrow_down", "rotation": 90}, "RIGHT": {"patternId": "S", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C407\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> N -> S -> W -> S -> W -> S -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_down, rotation=270, flipVertical=true\n- step 2: patternId=8, rotation=180, flipVertical=true\n- step 3: patternId=B, rotation=0, flipVertical=true\n- step 4: patternId=8, rotation=180, flipVertical=true\n- step 5: patternId=S, rotation=270, flipVertical=true\n- step 6: patternId=U, rotation=270, flipVertical=true\n- step 7: patternId=2, rotation=90, flipVertical=true\n- step 8: patternId=arrow_down, rotation=0, flipVertical=true\n- step 9: patternId=B, rotation=0, flipVertical=true\n- step 10: patternId=2, rotation=180, flipVertical=true\n- allowed patternId values for this task: arrow_down, 8, B, S, U, 2, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C407"} +{"sample_id": "C408", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> S -> S -> W -> N -> W -> S -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "S", "S", "W", "N", "W", "S", "S", "W"], "observed_path_faces": [{"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C408_path_sequence.png"}, "metadata": {"level_id": 408, "name": "Reconstruct 408", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-408.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["2", "M", "L", "Z", "Q", "A"], "start_x": 5, "start_y": 1, "grid_width": 7, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "2", "rotation": 180}, "BOTTOM": {"patternId": "A", "rotation": 180}, "FRONT": {"patternId": "M", "rotation": 270}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "Q", "rotation": 0}, "RIGHT": {"patternId": "L", "rotation": 270}}, "bottom_faces": [{"patternId": "A", "rotation": 180, "x": 5, "y": 1}, {"patternId": "M", "rotation": 270, "x": 5, "y": 2}, {"patternId": "Q", "rotation": 0, "x": 4, "y": 2}, {"patternId": "2", "rotation": 90, "x": 4, "y": 3}, {"patternId": "L", "rotation": 90, "x": 4, "y": 4}, {"patternId": "Z", "rotation": 270, "x": 3, "y": 4}, {"patternId": "2", "rotation": 180, "x": 3, "y": 3}, {"patternId": "Q", "rotation": 90, "x": 2, "y": 3}, {"patternId": "Z", "rotation": 180, "x": 2, "y": 4}, {"patternId": "L", "rotation": 0, "x": 2, "y": 5}, {"patternId": "A", "rotation": 180, "x": 1, "y": 5}], "slot_sequence": ["FRONT", "LEFT", "TOP", "RIGHT", "BACK", "TOP", "LEFT", "BACK", "RIGHT", "BOTTOM"], "required_slots": ["FRONT", "LEFT", "TOP", "RIGHT", "BACK", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "2", "rotation": 180}, "BOTTOM": {"patternId": "A", "rotation": 180}, "FRONT": {"patternId": "M", "rotation": 270}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "Q", "rotation": 90}, "RIGHT": {"patternId": "L", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "2", "rotation": 180}, "BOTTOM": {"patternId": "A", "rotation": 180}, "FRONT": {"patternId": "M", "rotation": 270}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "Q", "rotation": 90}, "RIGHT": {"patternId": "L", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C408\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> S -> S -> W -> N -> W -> S -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=M, rotation=270, flipVertical=true\n- step 2: patternId=Q, rotation=0, flipVertical=true\n- step 3: patternId=2, rotation=90, flipVertical=true\n- step 4: patternId=L, rotation=90, flipVertical=true\n- step 5: patternId=Z, rotation=270, flipVertical=true\n- step 6: patternId=2, rotation=180, flipVertical=true\n- step 7: patternId=Q, rotation=90, flipVertical=true\n- step 8: patternId=Z, rotation=180, flipVertical=true\n- step 9: patternId=L, rotation=0, flipVertical=true\n- step 10: patternId=A, rotation=180, flipVertical=true\n- allowed patternId values for this task: M, Q, 2, L, Z, A, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C408"} +{"sample_id": "C409", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> S -> E -> S -> E -> E -> S -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "S", "E", "S", "E", "E", "S", "S", "E"], "observed_path_faces": [{"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C409_path_sequence.png"}, "metadata": {"level_id": 409, "name": "Reconstruct 409", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-409.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["N", "V", "P", "A", "M", "K"], "start_x": 2, "start_y": 2, "grid_width": 7, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "N", "rotation": 180}, "BOTTOM": {"patternId": "K", "rotation": 270}, "FRONT": {"patternId": "V", "rotation": 270}, "BACK": {"patternId": "A", "rotation": 0}, "LEFT": {"patternId": "M", "rotation": 90}, "RIGHT": {"patternId": "P", "rotation": 90}}, "bottom_faces": [{"patternId": "K", "rotation": 270, "x": 2, "y": 2}, {"patternId": "A", "rotation": 180, "x": 2, "y": 1}, {"patternId": "M", "rotation": 270, "x": 1, "y": 1}, {"patternId": "K", "rotation": 180, "x": 1, "y": 2}, {"patternId": "A", "rotation": 90, "x": 2, "y": 2}, {"patternId": "P", "rotation": 180, "x": 2, "y": 3}, {"patternId": "N", "rotation": 0, "x": 3, "y": 3}, {"patternId": "M", "rotation": 0, "x": 4, "y": 3}, {"patternId": "V", "rotation": 180, "x": 4, "y": 4}, {"patternId": "P", "rotation": 0, "x": 4, "y": 5}, {"patternId": "K", "rotation": 90, "x": 5, "y": 5}], "slot_sequence": ["BACK", "LEFT", "BOTTOM", "BACK", "RIGHT", "TOP", "LEFT", "FRONT", "RIGHT", "BOTTOM"], "required_slots": ["BACK", "LEFT", "BOTTOM", "RIGHT", "TOP", "FRONT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "N", "rotation": 180}, "BOTTOM": {"patternId": "K", "rotation": 270}, "FRONT": {"patternId": "V", "rotation": 270}, "BACK": {"patternId": "A", "rotation": 180}, "LEFT": {"patternId": "M", "rotation": 180}, "RIGHT": {"patternId": "P", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "N", "rotation": 180}, "BOTTOM": {"patternId": "K", "rotation": 270}, "FRONT": {"patternId": "V", "rotation": 270}, "BACK": {"patternId": "A", "rotation": 180}, "LEFT": {"patternId": "M", "rotation": 180}, "RIGHT": {"patternId": "P", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C409\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> S -> E -> S -> E -> E -> S -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=A, rotation=180, flipVertical=true\n- step 2: patternId=M, rotation=270, flipVertical=true\n- step 3: patternId=K, rotation=180, flipVertical=true\n- step 4: patternId=A, rotation=90, flipVertical=true\n- step 5: patternId=P, rotation=180, flipVertical=true\n- step 6: patternId=N, rotation=0, flipVertical=true\n- step 7: patternId=M, rotation=0, flipVertical=true\n- step 8: patternId=V, rotation=180, flipVertical=true\n- step 9: patternId=P, rotation=0, flipVertical=true\n- step 10: patternId=K, rotation=90, flipVertical=true\n- allowed patternId values for this task: A, M, K, P, N, V, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C409"} +{"sample_id": "C410", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> E -> E -> E -> S -> S -> S -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "E", "E", "E", "S", "S", "S", "N", "W"], "observed_path_faces": [{"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C410_path_sequence.png"}, "metadata": {"level_id": 410, "name": "Reconstruct 410", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-410.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["3", "B", "A", "4", "C", "circle"], "start_x": 1, "start_y": 3, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "3", "rotation": 0}, "BOTTOM": {"patternId": "circle", "rotation": 90}, "FRONT": {"patternId": "B", "rotation": 270}, "BACK": {"patternId": "4", "rotation": 0}, "LEFT": {"patternId": "C", "rotation": 180}, "RIGHT": {"patternId": "A", "rotation": 180}}, "bottom_faces": [{"patternId": "circle", "rotation": 90, "x": 1, "y": 3}, {"patternId": "4", "rotation": 180, "x": 1, "y": 2}, {"patternId": "3", "rotation": 0, "x": 1, "y": 1}, {"patternId": "A", "rotation": 90, "x": 2, "y": 1}, {"patternId": "circle", "rotation": 270, "x": 3, "y": 1}, {"patternId": "C", "rotation": 270, "x": 4, "y": 1}, {"patternId": "4", "rotation": 90, "x": 4, "y": 2}, {"patternId": "A", "rotation": 270, "x": 4, "y": 3}, {"patternId": "B", "rotation": 0, "x": 4, "y": 4}, {"patternId": "A", "rotation": 270, "x": 4, "y": 3}, {"patternId": "circle", "rotation": 90, "x": 3, "y": 3}], "slot_sequence": ["BACK", "TOP", "RIGHT", "BOTTOM", "LEFT", "BACK", "RIGHT", "FRONT", "RIGHT", "BOTTOM"], "required_slots": ["BACK", "TOP", "RIGHT", "BOTTOM", "LEFT", "FRONT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "3", "rotation": 0}, "BOTTOM": {"patternId": "circle", "rotation": 90}, "FRONT": {"patternId": "B", "rotation": 270}, "BACK": {"patternId": "4", "rotation": 180}, "LEFT": {"patternId": "C", "rotation": 270}, "RIGHT": {"patternId": "A", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "3", "rotation": 0}, "BOTTOM": {"patternId": "circle", "rotation": 90}, "FRONT": {"patternId": "B", "rotation": 270}, "BACK": {"patternId": "4", "rotation": 180}, "LEFT": {"patternId": "C", "rotation": 270}, "RIGHT": {"patternId": "A", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C410\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> E -> E -> E -> S -> S -> S -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=4, rotation=180, flipVertical=true\n- step 2: patternId=3, rotation=0, flipVertical=true\n- step 3: patternId=A, rotation=90, flipVertical=true\n- step 4: patternId=circle, rotation=270, flipVertical=true\n- step 5: patternId=C, rotation=270, flipVertical=true\n- step 6: patternId=4, rotation=90, flipVertical=true\n- step 7: patternId=A, rotation=270, flipVertical=true\n- step 8: patternId=B, rotation=0, flipVertical=true\n- step 9: patternId=A, rotation=270, flipVertical=true\n- step 10: patternId=circle, rotation=90, flipVertical=true\n- allowed patternId values for this task: 4, 3, A, circle, C, B, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C410"} +{"sample_id": "C411", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> E -> S -> E -> S -> W -> S -> W -> S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "E", "S", "E", "S", "W", "S", "W", "S", "N"], "observed_path_faces": [{"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C411_path_sequence.png"}, "metadata": {"level_id": 411, "name": "Reconstruct 411", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-411.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["W", "O", "heart", "6", "arrow_up", "Z"], "start_x": 2, "start_y": 1, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "W", "rotation": 180}, "BOTTOM": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "O", "rotation": 90}, "BACK": {"patternId": "6", "rotation": 270}, "LEFT": {"patternId": "arrow_up", "rotation": 0}, "RIGHT": {"patternId": "heart", "rotation": 270}}, "bottom_faces": [{"patternId": "Z", "rotation": 270, "x": 2, "y": 1}, {"patternId": "arrow_up", "rotation": 270, "x": 1, "y": 1}, {"patternId": "Z", "rotation": 270, "x": 2, "y": 1}, {"patternId": "O", "rotation": 90, "x": 2, "y": 2}, {"patternId": "heart", "rotation": 270, "x": 3, "y": 2}, {"patternId": "W", "rotation": 270, "x": 3, "y": 3}, {"patternId": "O", "rotation": 180, "x": 2, "y": 3}, {"patternId": "arrow_up", "rotation": 90, "x": 2, "y": 4}, {"patternId": "Z", "rotation": 90, "x": 1, "y": 4}, {"patternId": "6", "rotation": 270, "x": 1, "y": 5}, {"patternId": "Z", "rotation": 90, "x": 1, "y": 4}], "slot_sequence": ["LEFT", "BOTTOM", "FRONT", "RIGHT", "TOP", "FRONT", "LEFT", "BOTTOM", "BACK", "BOTTOM"], "required_slots": ["LEFT", "BOTTOM", "FRONT", "RIGHT", "TOP", "BACK"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "W", "rotation": 180}, "BOTTOM": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "O", "rotation": 90}, "BACK": {"patternId": "6", "rotation": 90}, "LEFT": {"patternId": "arrow_up", "rotation": 90}, "RIGHT": {"patternId": "heart", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "W", "rotation": 180}, "BOTTOM": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "O", "rotation": 90}, "BACK": {"patternId": "6", "rotation": 90}, "LEFT": {"patternId": "arrow_up", "rotation": 90}, "RIGHT": {"patternId": "heart", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C411\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): W -> E -> S -> E -> S -> W -> S -> W -> S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_up, rotation=270, flipVertical=true\n- step 2: patternId=Z, rotation=270, flipVertical=true\n- step 3: patternId=O, rotation=90, flipVertical=true\n- step 4: patternId=heart, rotation=270, flipVertical=true\n- step 5: patternId=W, rotation=270, flipVertical=true\n- step 6: patternId=O, rotation=180, flipVertical=true\n- step 7: patternId=arrow_up, rotation=90, flipVertical=true\n- step 8: patternId=Z, rotation=90, flipVertical=true\n- step 9: patternId=6, rotation=270, flipVertical=true\n- step 10: patternId=Z, rotation=90, flipVertical=true\n- allowed patternId values for this task: arrow_up, Z, O, heart, W, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C411"} +{"sample_id": "C412", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> E -> E -> S -> W -> W -> W -> N -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "E", "E", "S", "W", "W", "W", "N", "S"], "observed_path_faces": [{"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C412_path_sequence.png"}, "metadata": {"level_id": 412, "name": "Reconstruct 412", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-412.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["U", "S", "1", "arrow_up", "1", "arrow_right"], "start_x": 1, "start_y": 2, "grid_width": 6, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "U", "rotation": 90}, "BOTTOM": {"patternId": "arrow_right", "rotation": 180}, "FRONT": {"patternId": "S", "rotation": 180}, "BACK": {"patternId": "arrow_up", "rotation": 270}, "LEFT": {"patternId": "1", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 90}}, "bottom_faces": [{"patternId": "arrow_right", "rotation": 180, "x": 1, "y": 2}, {"patternId": "arrow_up", "rotation": 90, "x": 1, "y": 1}, {"patternId": "1", "rotation": 270, "x": 2, "y": 1}, {"patternId": "S", "rotation": 0, "x": 3, "y": 1}, {"patternId": "1", "rotation": 180, "x": 4, "y": 1}, {"patternId": "arrow_right", "rotation": 90, "x": 4, "y": 2}, {"patternId": "S", "rotation": 90, "x": 3, "y": 2}, {"patternId": "U", "rotation": 0, "x": 2, "y": 2}, {"patternId": "arrow_up", "rotation": 0, "x": 1, "y": 2}, {"patternId": "1", "rotation": 90, "x": 1, "y": 1}, {"patternId": "arrow_up", "rotation": 0, "x": 1, "y": 2}], "slot_sequence": ["BACK", "RIGHT", "FRONT", "LEFT", "BOTTOM", "FRONT", "TOP", "BACK", "LEFT", "BACK"], "required_slots": ["BACK", "RIGHT", "FRONT", "LEFT", "BOTTOM", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "U", "rotation": 90}, "BOTTOM": {"patternId": "arrow_right", "rotation": 180}, "FRONT": {"patternId": "S", "rotation": 180}, "BACK": {"patternId": "arrow_up", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 90}, "RIGHT": {"patternId": "1", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "U", "rotation": 90}, "BOTTOM": {"patternId": "arrow_right", "rotation": 180}, "FRONT": {"patternId": "S", "rotation": 180}, "BACK": {"patternId": "arrow_up", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 90}, "RIGHT": {"patternId": "1", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C412\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> E -> E -> S -> W -> W -> W -> N -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_up, rotation=90, flipVertical=true\n- step 2: patternId=1, rotation=270, flipVertical=true\n- step 3: patternId=S, rotation=0, flipVertical=true\n- step 4: patternId=1, rotation=180, flipVertical=true\n- step 5: patternId=arrow_right, rotation=90, flipVertical=true\n- step 6: patternId=S, rotation=90, flipVertical=true\n- step 7: patternId=U, rotation=0, flipVertical=true\n- step 8: patternId=arrow_up, rotation=0, flipVertical=true\n- step 9: patternId=1, rotation=90, flipVertical=true\n- step 10: patternId=arrow_up, rotation=0, flipVertical=true\n- allowed patternId values for this task: arrow_up, 1, S, arrow_right, U, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C412"} +{"sample_id": "C413", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> N -> N -> W -> N -> N -> W -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "N", "N", "W", "N", "N", "W", "E", "S"], "observed_path_faces": [{"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C413_path_sequence.png"}, "metadata": {"level_id": 413, "name": "Reconstruct 413", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-413.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["O", "5", "5", "circle", "arrow_left", "1"], "start_x": 4, "start_y": 4, "grid_width": 6, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "O", "rotation": 180}, "BOTTOM": {"patternId": "1", "rotation": 90}, "FRONT": {"patternId": "5", "rotation": 90}, "BACK": {"patternId": "circle", "rotation": 90}, "LEFT": {"patternId": "arrow_left", "rotation": 0}, "RIGHT": {"patternId": "5", "rotation": 90}}, "bottom_faces": [{"patternId": "1", "rotation": 90, "x": 4, "y": 4}, {"patternId": "5", "rotation": 90, "x": 4, "y": 5}, {"patternId": "arrow_left", "rotation": 0, "x": 3, "y": 5}, {"patternId": "1", "rotation": 180, "x": 3, "y": 4}, {"patternId": "5", "rotation": 270, "x": 3, "y": 3}, {"patternId": "circle", "rotation": 270, "x": 2, "y": 3}, {"patternId": "O", "rotation": 180, "x": 2, "y": 2}, {"patternId": "5", "rotation": 90, "x": 2, "y": 1}, {"patternId": "arrow_left", "rotation": 0, "x": 1, "y": 1}, {"patternId": "5", "rotation": 90, "x": 2, "y": 1}, {"patternId": "O", "rotation": 180, "x": 2, "y": 2}], "slot_sequence": ["FRONT", "LEFT", "BOTTOM", "RIGHT", "BACK", "TOP", "FRONT", "LEFT", "FRONT", "TOP"], "required_slots": ["FRONT", "LEFT", "BOTTOM", "RIGHT", "BACK", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "O", "rotation": 180}, "BOTTOM": {"patternId": "1", "rotation": 90}, "FRONT": {"patternId": "5", "rotation": 90}, "BACK": {"patternId": "circle", "rotation": 270}, "LEFT": {"patternId": "arrow_left", "rotation": 90}, "RIGHT": {"patternId": "5", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 180}, "BOTTOM": {"patternId": "1", "rotation": 90}, "FRONT": {"patternId": "5", "rotation": 90}, "BACK": {"patternId": "circle", "rotation": 270}, "LEFT": {"patternId": "arrow_left", "rotation": 90}, "RIGHT": {"patternId": "5", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C413\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> N -> N -> W -> N -> N -> W -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=5, rotation=90, flipVertical=true\n- step 2: patternId=arrow_left, rotation=0, flipVertical=true\n- step 3: patternId=1, rotation=180, flipVertical=true\n- step 4: patternId=5, rotation=270, flipVertical=true\n- step 5: patternId=circle, rotation=270, flipVertical=true\n- step 6: patternId=O, rotation=180, flipVertical=true\n- step 7: patternId=5, rotation=90, flipVertical=true\n- step 8: patternId=arrow_left, rotation=0, flipVertical=true\n- step 9: patternId=5, rotation=90, flipVertical=true\n- step 10: patternId=O, rotation=180, flipVertical=true\n- allowed patternId values for this task: 5, arrow_left, 1, circle, O, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C413"} +{"sample_id": "C414", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> W -> W -> S -> S -> N -> E -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "W", "W", "S", "S", "N", "E", "E", "E"], "observed_path_faces": [{"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C414_path_sequence.png"}, "metadata": {"level_id": 414, "name": "Reconstruct 414", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-414.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["B", "triangle", "star", "star", "plus", "9"], "start_x": 4, "start_y": 2, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "B", "rotation": 270}, "BOTTOM": {"patternId": "9", "rotation": 270}, "FRONT": {"patternId": "triangle", "rotation": 180}, "BACK": {"patternId": "star", "rotation": 0}, "LEFT": {"patternId": "plus", "rotation": 90}, "RIGHT": {"patternId": "star", "rotation": 270}}, "bottom_faces": [{"patternId": "9", "rotation": 270, "x": 4, "y": 2}, {"patternId": "plus", "rotation": 0, "x": 3, "y": 2}, {"patternId": "star", "rotation": 270, "x": 3, "y": 1}, {"patternId": "B", "rotation": 0, "x": 2, "y": 1}, {"patternId": "triangle", "rotation": 270, "x": 1, "y": 1}, {"patternId": "plus", "rotation": 180, "x": 1, "y": 2}, {"patternId": "star", "rotation": 90, "x": 1, "y": 3}, {"patternId": "plus", "rotation": 180, "x": 1, "y": 2}, {"patternId": "B", "rotation": 270, "x": 2, "y": 2}, {"patternId": "star", "rotation": 180, "x": 3, "y": 2}, {"patternId": "9", "rotation": 90, "x": 4, "y": 2}], "slot_sequence": ["LEFT", "BACK", "TOP", "FRONT", "LEFT", "BACK", "LEFT", "TOP", "RIGHT", "BOTTOM"], "required_slots": ["LEFT", "BACK", "TOP", "FRONT", "RIGHT", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "B", "rotation": 270}, "BOTTOM": {"patternId": "9", "rotation": 270}, "FRONT": {"patternId": "triangle", "rotation": 180}, "BACK": {"patternId": "star", "rotation": 180}, "LEFT": {"patternId": "plus", "rotation": 180}, "RIGHT": {"patternId": "star", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "B", "rotation": 270}, "BOTTOM": {"patternId": "9", "rotation": 270}, "FRONT": {"patternId": "triangle", "rotation": 180}, "BACK": {"patternId": "star", "rotation": 180}, "LEFT": {"patternId": "plus", "rotation": 180}, "RIGHT": {"patternId": "star", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C414\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> W -> W -> S -> S -> N -> E -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=plus, rotation=0, flipVertical=true\n- step 2: patternId=star, rotation=270, flipVertical=true\n- step 3: patternId=B, rotation=0, flipVertical=true\n- step 4: patternId=triangle, rotation=270, flipVertical=true\n- step 5: patternId=plus, rotation=180, flipVertical=true\n- step 6: patternId=star, rotation=90, flipVertical=true\n- step 7: patternId=plus, rotation=180, flipVertical=true\n- step 8: patternId=B, rotation=270, flipVertical=true\n- step 9: patternId=star, rotation=180, flipVertical=true\n- step 10: patternId=9, rotation=90, flipVertical=true\n- allowed patternId values for this task: plus, star, B, triangle, 9, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C414"} +{"sample_id": "C415", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> E -> S -> S -> N -> W -> W -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "E", "S", "S", "N", "W", "W", "N", "W"], "observed_path_faces": [{"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C415_path_sequence.png"}, "metadata": {"level_id": 415, "name": "Reconstruct 415", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-415.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["smile", "G", "8", "Y", "arrow_down", "P"], "start_x": 3, "start_y": 1, "grid_width": 6, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "smile", "rotation": 270}, "BOTTOM": {"patternId": "P", "rotation": 180}, "FRONT": {"patternId": "G", "rotation": 90}, "BACK": {"patternId": "Y", "rotation": 90}, "LEFT": {"patternId": "arrow_down", "rotation": 90}, "RIGHT": {"patternId": "8", "rotation": 0}}, "bottom_faces": [{"patternId": "P", "rotation": 180, "x": 3, "y": 1}, {"patternId": "G", "rotation": 90, "x": 3, "y": 2}, {"patternId": "smile", "rotation": 270, "x": 3, "y": 3}, {"patternId": "8", "rotation": 270, "x": 4, "y": 3}, {"patternId": "Y", "rotation": 0, "x": 4, "y": 4}, {"patternId": "arrow_down", "rotation": 0, "x": 4, "y": 5}, {"patternId": "Y", "rotation": 0, "x": 4, "y": 4}, {"patternId": "smile", "rotation": 0, "x": 3, "y": 4}, {"patternId": "G", "rotation": 180, "x": 2, "y": 4}, {"patternId": "8", "rotation": 90, "x": 2, "y": 3}, {"patternId": "P", "rotation": 180, "x": 1, "y": 3}], "slot_sequence": ["FRONT", "TOP", "RIGHT", "BACK", "LEFT", "BACK", "TOP", "FRONT", "RIGHT", "BOTTOM"], "required_slots": ["FRONT", "TOP", "RIGHT", "BACK", "LEFT", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "smile", "rotation": 270}, "BOTTOM": {"patternId": "P", "rotation": 180}, "FRONT": {"patternId": "G", "rotation": 90}, "BACK": {"patternId": "Y", "rotation": 270}, "LEFT": {"patternId": "arrow_down", "rotation": 180}, "RIGHT": {"patternId": "8", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 270}, "BOTTOM": {"patternId": "P", "rotation": 180}, "FRONT": {"patternId": "G", "rotation": 90}, "BACK": {"patternId": "Y", "rotation": 270}, "LEFT": {"patternId": "arrow_down", "rotation": 180}, "RIGHT": {"patternId": "8", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C415\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> E -> S -> S -> N -> W -> W -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=G, rotation=90, flipVertical=true\n- step 2: patternId=smile, rotation=270, flipVertical=true\n- step 3: patternId=8, rotation=270, flipVertical=true\n- step 4: patternId=Y, rotation=0, flipVertical=true\n- step 5: patternId=arrow_down, rotation=0, flipVertical=true\n- step 6: patternId=Y, rotation=0, flipVertical=true\n- step 7: patternId=smile, rotation=0, flipVertical=true\n- step 8: patternId=G, rotation=180, flipVertical=true\n- step 9: patternId=8, rotation=90, flipVertical=true\n- step 10: patternId=P, rotation=180, flipVertical=true\n- allowed patternId values for this task: G, smile, 8, Y, arrow_down, P, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C415"} +{"sample_id": "C416", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> S -> N -> W -> W -> W -> E -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "S", "N", "W", "W", "W", "E", "E", "S"], "observed_path_faces": [{"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C416_path_sequence.png"}, "metadata": {"level_id": 416, "name": "Reconstruct 416", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-416.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["G", "plus", "smile", "arrow_down", "6", "X"], "start_x": 5, "start_y": 1, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "G", "rotation": 180}, "BOTTOM": {"patternId": "X", "rotation": 180}, "FRONT": {"patternId": "plus", "rotation": 270}, "BACK": {"patternId": "arrow_down", "rotation": 0}, "LEFT": {"patternId": "6", "rotation": 0}, "RIGHT": {"patternId": "smile", "rotation": 270}}, "bottom_faces": [{"patternId": "X", "rotation": 180, "x": 5, "y": 1}, {"patternId": "plus", "rotation": 270, "x": 5, "y": 2}, {"patternId": "6", "rotation": 0, "x": 4, "y": 2}, {"patternId": "G", "rotation": 90, "x": 4, "y": 3}, {"patternId": "6", "rotation": 0, "x": 4, "y": 2}, {"patternId": "arrow_down", "rotation": 0, "x": 3, "y": 2}, {"patternId": "smile", "rotation": 270, "x": 2, "y": 2}, {"patternId": "plus", "rotation": 270, "x": 1, "y": 2}, {"patternId": "smile", "rotation": 270, "x": 2, "y": 2}, {"patternId": "arrow_down", "rotation": 0, "x": 3, "y": 2}, {"patternId": "G", "rotation": 0, "x": 3, "y": 3}], "slot_sequence": ["FRONT", "LEFT", "TOP", "LEFT", "BACK", "RIGHT", "FRONT", "RIGHT", "BACK", "TOP"], "required_slots": ["FRONT", "LEFT", "TOP", "BACK", "RIGHT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "G", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "plus", "rotation": 270}, "BACK": {"patternId": "arrow_down", "rotation": 180}, "LEFT": {"patternId": "6", "rotation": 90}, "RIGHT": {"patternId": "smile", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "G", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "plus", "rotation": 270}, "BACK": {"patternId": "arrow_down", "rotation": 180}, "LEFT": {"patternId": "6", "rotation": 90}, "RIGHT": {"patternId": "smile", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C416\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> S -> N -> W -> W -> W -> E -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=plus, rotation=270, flipVertical=true\n- step 2: patternId=6, rotation=0, flipVertical=true\n- step 3: patternId=G, rotation=90, flipVertical=true\n- step 4: patternId=6, rotation=0, flipVertical=true\n- step 5: patternId=arrow_down, rotation=0, flipVertical=true\n- step 6: patternId=smile, rotation=270, flipVertical=true\n- step 7: patternId=plus, rotation=270, flipVertical=true\n- step 8: patternId=smile, rotation=270, flipVertical=true\n- step 9: patternId=arrow_down, rotation=0, flipVertical=true\n- step 10: patternId=G, rotation=0, flipVertical=true\n- allowed patternId values for this task: plus, 6, G, arrow_down, smile, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C416"} +{"sample_id": "C417", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> S -> E -> E -> N -> E -> N -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "S", "E", "E", "N", "E", "N", "W", "W"], "observed_path_faces": [{"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C417_path_sequence.png"}, "metadata": {"level_id": 417, "name": "Reconstruct 417", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-417.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["K", "heart", "4", "Z", "B", "square"], "start_x": 1, "start_y": 3, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "K", "rotation": 90}, "BOTTOM": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "heart", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "B", "rotation": 90}, "RIGHT": {"patternId": "4", "rotation": 0}}, "bottom_faces": [{"patternId": "square", "rotation": 90, "x": 1, "y": 3}, {"patternId": "Z", "rotation": 90, "x": 1, "y": 2}, {"patternId": "4", "rotation": 180, "x": 2, "y": 2}, {"patternId": "square", "rotation": 180, "x": 2, "y": 3}, {"patternId": "heart", "rotation": 270, "x": 3, "y": 3}, {"patternId": "K", "rotation": 180, "x": 4, "y": 3}, {"patternId": "4", "rotation": 0, "x": 4, "y": 2}, {"patternId": "Z", "rotation": 270, "x": 5, "y": 2}, {"patternId": "square", "rotation": 270, "x": 5, "y": 1}, {"patternId": "4", "rotation": 270, "x": 4, "y": 1}, {"patternId": "K", "rotation": 90, "x": 3, "y": 1}], "slot_sequence": ["BACK", "RIGHT", "BOTTOM", "FRONT", "TOP", "RIGHT", "BACK", "BOTTOM", "RIGHT", "TOP"], "required_slots": ["BACK", "RIGHT", "BOTTOM", "FRONT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "K", "rotation": 90}, "BOTTOM": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "heart", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "4", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "K", "rotation": 90}, "BOTTOM": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "heart", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "4", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C417\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> S -> E -> E -> N -> E -> N -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Z, rotation=90, flipVertical=true\n- step 2: patternId=4, rotation=180, flipVertical=true\n- step 3: patternId=square, rotation=180, flipVertical=true\n- step 4: patternId=heart, rotation=270, flipVertical=true\n- step 5: patternId=K, rotation=180, flipVertical=true\n- step 6: patternId=4, rotation=0, flipVertical=true\n- step 7: patternId=Z, rotation=270, flipVertical=true\n- step 8: patternId=square, rotation=270, flipVertical=true\n- step 9: patternId=4, rotation=270, flipVertical=true\n- step 10: patternId=K, rotation=90, flipVertical=true\n- allowed patternId values for this task: Z, 4, square, heart, K, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C417"} +{"sample_id": "C418", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> S -> W -> E -> S -> W -> N -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "S", "W", "E", "S", "W", "N", "W", "W"], "observed_path_faces": [{"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C418_path_sequence.png"}, "metadata": {"level_id": 418, "name": "Reconstruct 418", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-418.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["plus", "N", "J", "1", "triangle", "arrow_right"], "start_x": 2, "start_y": 1, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "plus", "rotation": 180}, "BOTTOM": {"patternId": "arrow_right", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 90}, "BACK": {"patternId": "1", "rotation": 0}, "LEFT": {"patternId": "triangle", "rotation": 0}, "RIGHT": {"patternId": "J", "rotation": 90}}, "bottom_faces": [{"patternId": "arrow_right", "rotation": 0, "x": 2, "y": 1}, {"patternId": "J", "rotation": 180, "x": 3, "y": 1}, {"patternId": "plus", "rotation": 0, "x": 4, "y": 1}, {"patternId": "N", "rotation": 270, "x": 4, "y": 2}, {"patternId": "J", "rotation": 270, "x": 3, "y": 2}, {"patternId": "N", "rotation": 270, "x": 4, "y": 2}, {"patternId": "arrow_right", "rotation": 180, "x": 4, "y": 3}, {"patternId": "J", "rotation": 0, "x": 3, "y": 3}, {"patternId": "N", "rotation": 0, "x": 3, "y": 2}, {"patternId": "plus", "rotation": 90, "x": 2, "y": 2}, {"patternId": "1", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["RIGHT", "TOP", "FRONT", "RIGHT", "FRONT", "BOTTOM", "RIGHT", "FRONT", "TOP", "BACK"], "required_slots": ["RIGHT", "TOP", "FRONT", "BOTTOM", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "plus", "rotation": 180}, "BOTTOM": {"patternId": "arrow_right", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 90}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "J", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "plus", "rotation": 180}, "BOTTOM": {"patternId": "arrow_right", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 90}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "J", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C418\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> S -> W -> E -> S -> W -> N -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=J, rotation=180, flipVertical=true\n- step 2: patternId=plus, rotation=0, flipVertical=true\n- step 3: patternId=N, rotation=270, flipVertical=true\n- step 4: patternId=J, rotation=270, flipVertical=true\n- step 5: patternId=N, rotation=270, flipVertical=true\n- step 6: patternId=arrow_right, rotation=180, flipVertical=true\n- step 7: patternId=J, rotation=0, flipVertical=true\n- step 8: patternId=N, rotation=0, flipVertical=true\n- step 9: patternId=plus, rotation=90, flipVertical=true\n- step 10: patternId=1, rotation=90, flipVertical=true\n- allowed patternId values for this task: J, plus, N, arrow_right, 1, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C418"} +{"sample_id": "C419", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> S -> W -> S -> E -> S -> E -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "S", "W", "S", "E", "S", "E", "E", "N"], "observed_path_faces": [{"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C419_path_sequence.png"}, "metadata": {"level_id": 419, "name": "Reconstruct 419", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-419.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["5", "H", "2", "3", "R", "diamond"], "start_x": 1, "start_y": 1, "grid_width": 6, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "5", "rotation": 270}, "BOTTOM": {"patternId": "diamond", "rotation": 270}, "FRONT": {"patternId": "H", "rotation": 90}, "BACK": {"patternId": "3", "rotation": 270}, "LEFT": {"patternId": "R", "rotation": 0}, "RIGHT": {"patternId": "2", "rotation": 0}}, "bottom_faces": [{"patternId": "diamond", "rotation": 270, "x": 1, "y": 1}, {"patternId": "H", "rotation": 90, "x": 1, "y": 2}, {"patternId": "2", "rotation": 0, "x": 2, "y": 2}, {"patternId": "5", "rotation": 0, "x": 2, "y": 3}, {"patternId": "H", "rotation": 180, "x": 1, "y": 3}, {"patternId": "R", "rotation": 90, "x": 1, "y": 4}, {"patternId": "5", "rotation": 270, "x": 2, "y": 4}, {"patternId": "3", "rotation": 90, "x": 2, "y": 5}, {"patternId": "2", "rotation": 180, "x": 3, "y": 5}, {"patternId": "H", "rotation": 270, "x": 4, "y": 5}, {"patternId": "5", "rotation": 90, "x": 4, "y": 4}], "slot_sequence": ["FRONT", "RIGHT", "TOP", "FRONT", "LEFT", "TOP", "BACK", "RIGHT", "FRONT", "TOP"], "required_slots": ["FRONT", "RIGHT", "TOP", "LEFT", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "5", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 90}, "BACK": {"patternId": "3", "rotation": 90}, "LEFT": {"patternId": "R", "rotation": 90}, "RIGHT": {"patternId": "2", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "5", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 90}, "BACK": {"patternId": "3", "rotation": 90}, "LEFT": {"patternId": "R", "rotation": 90}, "RIGHT": {"patternId": "2", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C419\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> S -> W -> S -> E -> S -> E -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=H, rotation=90, flipVertical=true\n- step 2: patternId=2, rotation=0, flipVertical=true\n- step 3: patternId=5, rotation=0, flipVertical=true\n- step 4: patternId=H, rotation=180, flipVertical=true\n- step 5: patternId=R, rotation=90, flipVertical=true\n- step 6: patternId=5, rotation=270, flipVertical=true\n- step 7: patternId=3, rotation=90, flipVertical=true\n- step 8: patternId=2, rotation=180, flipVertical=true\n- step 9: patternId=H, rotation=270, flipVertical=true\n- step 10: patternId=5, rotation=90, flipVertical=true\n- allowed patternId values for this task: H, 2, 5, R, 3, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C419"} +{"sample_id": "C420", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> W -> W -> N -> E -> N -> E -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "W", "W", "N", "E", "N", "E", "S", "E"], "observed_path_faces": [{"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C420_path_sequence.png"}, "metadata": {"level_id": 420, "name": "Reconstruct 420", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-420.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Z", "H", "I", "K", "I", "8"], "start_x": 2, "start_y": 4, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "Z", "rotation": 270}, "BOTTOM": {"patternId": "8", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 180}, "BACK": {"patternId": "K", "rotation": 90}, "LEFT": {"patternId": "I", "rotation": 180}, "RIGHT": {"patternId": "I", "rotation": 270}}, "bottom_faces": [{"patternId": "8", "rotation": 0, "x": 2, "y": 4}, {"patternId": "I", "rotation": 0, "x": 3, "y": 4}, {"patternId": "K", "rotation": 180, "x": 3, "y": 3}, {"patternId": "8", "rotation": 270, "x": 2, "y": 3}, {"patternId": "H", "rotation": 90, "x": 1, "y": 3}, {"patternId": "I", "rotation": 90, "x": 1, "y": 2}, {"patternId": "8", "rotation": 0, "x": 2, "y": 2}, {"patternId": "K", "rotation": 270, "x": 2, "y": 1}, {"patternId": "I", "rotation": 90, "x": 3, "y": 1}, {"patternId": "8", "rotation": 90, "x": 3, "y": 2}, {"patternId": "H", "rotation": 270, "x": 4, "y": 2}], "slot_sequence": ["RIGHT", "BACK", "BOTTOM", "FRONT", "LEFT", "BOTTOM", "BACK", "RIGHT", "BOTTOM", "FRONT"], "required_slots": ["RIGHT", "BACK", "BOTTOM", "FRONT", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 180}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "I", "rotation": 270}, "RIGHT": {"patternId": "I", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 180}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "I", "rotation": 270}, "RIGHT": {"patternId": "I", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C420\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> W -> W -> N -> E -> N -> E -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=I, rotation=0, flipVertical=true\n- step 2: patternId=K, rotation=180, flipVertical=true\n- step 3: patternId=8, rotation=270, flipVertical=true\n- step 4: patternId=H, rotation=90, flipVertical=true\n- step 5: patternId=I, rotation=90, flipVertical=true\n- step 6: patternId=8, rotation=0, flipVertical=true\n- step 7: patternId=K, rotation=270, flipVertical=true\n- step 8: patternId=I, rotation=90, flipVertical=true\n- step 9: patternId=8, rotation=90, flipVertical=true\n- step 10: patternId=H, rotation=270, flipVertical=true\n- allowed patternId values for this task: I, K, 8, H, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C420"} +{"sample_id": "C421", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> W -> S -> E -> W -> E -> N -> W -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "W", "S", "E", "W", "E", "N", "W", "N", "N"], "observed_path_faces": [{"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C421_path_sequence.png"}, "metadata": {"level_id": 421, "name": "Reconstruct 421", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-421.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["8", "V", "C", "M", "3", "W"], "start_x": 1, "start_y": 3, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "8", "rotation": 270}, "BOTTOM": {"patternId": "W", "rotation": 270}, "FRONT": {"patternId": "V", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 270}, "LEFT": {"patternId": "3", "rotation": 180}, "RIGHT": {"patternId": "C", "rotation": 0}}, "bottom_faces": [{"patternId": "W", "rotation": 270, "x": 1, "y": 3}, {"patternId": "C", "rotation": 90, "x": 2, "y": 3}, {"patternId": "W", "rotation": 270, "x": 1, "y": 3}, {"patternId": "V", "rotation": 0, "x": 1, "y": 4}, {"patternId": "C", "rotation": 0, "x": 2, "y": 4}, {"patternId": "V", "rotation": 0, "x": 1, "y": 4}, {"patternId": "C", "rotation": 0, "x": 2, "y": 4}, {"patternId": "W", "rotation": 180, "x": 2, "y": 3}, {"patternId": "V", "rotation": 270, "x": 1, "y": 3}, {"patternId": "3", "rotation": 90, "x": 1, "y": 2}, {"patternId": "M", "rotation": 180, "x": 1, "y": 1}], "slot_sequence": ["RIGHT", "BOTTOM", "FRONT", "RIGHT", "FRONT", "RIGHT", "BOTTOM", "FRONT", "LEFT", "BACK"], "required_slots": ["RIGHT", "BOTTOM", "FRONT", "LEFT", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 270}, "FRONT": {"patternId": "V", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "3", "rotation": 270}, "RIGHT": {"patternId": "C", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 270}, "FRONT": {"patternId": "V", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "3", "rotation": 270}, "RIGHT": {"patternId": "C", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C421\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> W -> S -> E -> W -> E -> N -> W -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=C, rotation=90, flipVertical=true\n- step 2: patternId=W, rotation=270, flipVertical=true\n- step 3: patternId=V, rotation=0, flipVertical=true\n- step 4: patternId=C, rotation=0, flipVertical=true\n- step 5: patternId=V, rotation=0, flipVertical=true\n- step 6: patternId=C, rotation=0, flipVertical=true\n- step 7: patternId=W, rotation=180, flipVertical=true\n- step 8: patternId=V, rotation=270, flipVertical=true\n- step 9: patternId=3, rotation=90, flipVertical=true\n- step 10: patternId=M, rotation=180, flipVertical=true\n- allowed patternId values for this task: C, W, V, 3, M, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C421"} +{"sample_id": "C422", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> N -> W -> W -> W -> S -> S -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "N", "W", "W", "W", "S", "S", "W", "S"], "observed_path_faces": [{"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C422_path_sequence.png"}, "metadata": {"level_id": 422, "name": "Reconstruct 422", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-422.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["5", "H", "E", "circle", "V", "1"], "start_x": 3, "start_y": 2, "grid_width": 7, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "1", "rotation": 90}, "FRONT": {"patternId": "H", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 90}, "LEFT": {"patternId": "V", "rotation": 0}, "RIGHT": {"patternId": "E", "rotation": 90}}, "bottom_faces": [{"patternId": "1", "rotation": 90, "x": 3, "y": 2}, {"patternId": "E", "rotation": 180, "x": 4, "y": 2}, {"patternId": "5", "rotation": 270, "x": 5, "y": 2}, {"patternId": "circle", "rotation": 90, "x": 5, "y": 1}, {"patternId": "E", "rotation": 90, "x": 4, "y": 1}, {"patternId": "H", "rotation": 0, "x": 3, "y": 1}, {"patternId": "V", "rotation": 0, "x": 2, "y": 1}, {"patternId": "5", "rotation": 0, "x": 2, "y": 2}, {"patternId": "E", "rotation": 270, "x": 2, "y": 3}, {"patternId": "circle", "rotation": 270, "x": 1, "y": 3}, {"patternId": "1", "rotation": 90, "x": 1, "y": 4}], "slot_sequence": ["RIGHT", "TOP", "BACK", "RIGHT", "FRONT", "LEFT", "TOP", "RIGHT", "BACK", "BOTTOM"], "required_slots": ["RIGHT", "TOP", "BACK", "FRONT", "LEFT", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "1", "rotation": 90}, "FRONT": {"patternId": "H", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 270}, "LEFT": {"patternId": "V", "rotation": 90}, "RIGHT": {"patternId": "E", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "1", "rotation": 90}, "FRONT": {"patternId": "H", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 270}, "LEFT": {"patternId": "V", "rotation": 90}, "RIGHT": {"patternId": "E", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C422\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> N -> W -> W -> W -> S -> S -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=E, rotation=180, flipVertical=true\n- step 2: patternId=5, rotation=270, flipVertical=true\n- step 3: patternId=circle, rotation=90, flipVertical=true\n- step 4: patternId=E, rotation=90, flipVertical=true\n- step 5: patternId=H, rotation=0, flipVertical=true\n- step 6: patternId=V, rotation=0, flipVertical=true\n- step 7: patternId=5, rotation=0, flipVertical=true\n- step 8: patternId=E, rotation=270, flipVertical=true\n- step 9: patternId=circle, rotation=270, flipVertical=true\n- step 10: patternId=1, rotation=90, flipVertical=true\n- allowed patternId values for this task: E, 5, circle, H, V, 1, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C422"} +{"sample_id": "C423", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> N -> E -> S -> E -> N -> W -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "N", "E", "S", "E", "N", "W", "N", "E"], "observed_path_faces": [{"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C423_path_sequence.png"}, "metadata": {"level_id": 423, "name": "Reconstruct 423", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-423.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["B", "heart", "F", "M", "Q", "F"], "start_x": 1, "start_y": 2, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "B", "rotation": 270}, "BOTTOM": {"patternId": "F", "rotation": 270}, "FRONT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "Q", "rotation": 90}, "RIGHT": {"patternId": "F", "rotation": 180}}, "bottom_faces": [{"patternId": "F", "rotation": 270, "x": 1, "y": 2}, {"patternId": "heart", "rotation": 270, "x": 1, "y": 3}, {"patternId": "F", "rotation": 180, "x": 2, "y": 3}, {"patternId": "F", "rotation": 180, "x": 2, "y": 2}, {"patternId": "M", "rotation": 90, "x": 3, "y": 2}, {"patternId": "F", "rotation": 270, "x": 3, "y": 3}, {"patternId": "B", "rotation": 90, "x": 4, "y": 3}, {"patternId": "M", "rotation": 0, "x": 4, "y": 2}, {"patternId": "F", "rotation": 180, "x": 3, "y": 2}, {"patternId": "F", "rotation": 180, "x": 3, "y": 1}, {"patternId": "M", "rotation": 90, "x": 4, "y": 1}], "slot_sequence": ["FRONT", "RIGHT", "BOTTOM", "BACK", "RIGHT", "TOP", "BACK", "RIGHT", "BOTTOM", "BACK"], "required_slots": ["FRONT", "RIGHT", "BOTTOM", "BACK", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "B", "rotation": 270}, "BOTTOM": {"patternId": "F", "rotation": 270}, "FRONT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "M", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "F", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "B", "rotation": 270}, "BOTTOM": {"patternId": "F", "rotation": 270}, "FRONT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "M", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "F", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C423\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> N -> E -> S -> E -> N -> W -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=heart, rotation=270, flipVertical=true\n- step 2: patternId=F, rotation=180, flipVertical=true\n- step 3: patternId=F, rotation=180, flipVertical=true\n- step 4: patternId=M, rotation=90, flipVertical=true\n- step 5: patternId=F, rotation=270, flipVertical=true\n- step 6: patternId=B, rotation=90, flipVertical=true\n- step 7: patternId=M, rotation=0, flipVertical=true\n- step 8: patternId=F, rotation=180, flipVertical=true\n- step 9: patternId=F, rotation=180, flipVertical=true\n- step 10: patternId=M, rotation=90, flipVertical=true\n- allowed patternId values for this task: heart, F, M, B, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C423"} +{"sample_id": "C424", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> N -> E -> N -> E -> E -> N -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "N", "E", "N", "E", "E", "N", "E", "N"], "observed_path_faces": [{"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C424_path_sequence.png"}, "metadata": {"level_id": 424, "name": "Reconstruct 424", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-424.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["A", "Z", "U", "diamond", "D", "heart"], "start_x": 2, "start_y": 6, "grid_width": 7, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "A", "rotation": 90}, "BOTTOM": {"patternId": "heart", "rotation": 90}, "FRONT": {"patternId": "Z", "rotation": 0}, "BACK": {"patternId": "diamond", "rotation": 90}, "LEFT": {"patternId": "D", "rotation": 90}, "RIGHT": {"patternId": "U", "rotation": 90}}, "bottom_faces": [{"patternId": "heart", "rotation": 90, "x": 2, "y": 6}, {"patternId": "D", "rotation": 0, "x": 1, "y": 6}, {"patternId": "diamond", "rotation": 0, "x": 1, "y": 5}, {"patternId": "U", "rotation": 0, "x": 1, "y": 4}, {"patternId": "heart", "rotation": 270, "x": 2, "y": 4}, {"patternId": "Z", "rotation": 180, "x": 2, "y": 3}, {"patternId": "D", "rotation": 270, "x": 3, "y": 3}, {"patternId": "diamond", "rotation": 270, "x": 4, "y": 3}, {"patternId": "A", "rotation": 90, "x": 4, "y": 2}, {"patternId": "U", "rotation": 0, "x": 5, "y": 2}, {"patternId": "Z", "rotation": 270, "x": 5, "y": 1}], "slot_sequence": ["LEFT", "BACK", "RIGHT", "BOTTOM", "FRONT", "LEFT", "BACK", "TOP", "RIGHT", "FRONT"], "required_slots": ["LEFT", "BACK", "RIGHT", "BOTTOM", "FRONT", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "A", "rotation": 90}, "BOTTOM": {"patternId": "heart", "rotation": 90}, "FRONT": {"patternId": "Z", "rotation": 0}, "BACK": {"patternId": "diamond", "rotation": 270}, "LEFT": {"patternId": "D", "rotation": 180}, "RIGHT": {"patternId": "U", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "A", "rotation": 90}, "BOTTOM": {"patternId": "heart", "rotation": 90}, "FRONT": {"patternId": "Z", "rotation": 0}, "BACK": {"patternId": "diamond", "rotation": 270}, "LEFT": {"patternId": "D", "rotation": 180}, "RIGHT": {"patternId": "U", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C424\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> N -> E -> N -> E -> E -> N -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=D, rotation=0, flipVertical=true\n- step 2: patternId=diamond, rotation=0, flipVertical=true\n- step 3: patternId=U, rotation=0, flipVertical=true\n- step 4: patternId=heart, rotation=270, flipVertical=true\n- step 5: patternId=Z, rotation=180, flipVertical=true\n- step 6: patternId=D, rotation=270, flipVertical=true\n- step 7: patternId=diamond, rotation=270, flipVertical=true\n- step 8: patternId=A, rotation=90, flipVertical=true\n- step 9: patternId=U, rotation=0, flipVertical=true\n- step 10: patternId=Z, rotation=270, flipVertical=true\n- allowed patternId values for this task: D, diamond, U, heart, Z, A, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C424"} +{"sample_id": "C425", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> W -> E -> E -> N -> N -> N -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "W", "E", "E", "N", "N", "N", "W", "S"], "observed_path_faces": [{"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C425_path_sequence.png"}, "metadata": {"level_id": 425, "name": "Reconstruct 425", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-425.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["I", "4", "O", "3", "I", "7"], "start_x": 3, "start_y": 3, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "I", "rotation": 90}, "BOTTOM": {"patternId": "7", "rotation": 90}, "FRONT": {"patternId": "4", "rotation": 90}, "BACK": {"patternId": "3", "rotation": 0}, "LEFT": {"patternId": "I", "rotation": 90}, "RIGHT": {"patternId": "O", "rotation": 180}}, "bottom_faces": [{"patternId": "7", "rotation": 90, "x": 3, "y": 3}, {"patternId": "4", "rotation": 90, "x": 3, "y": 4}, {"patternId": "I", "rotation": 90, "x": 2, "y": 4}, {"patternId": "3", "rotation": 0, "x": 1, "y": 4}, {"patternId": "I", "rotation": 90, "x": 2, "y": 4}, {"patternId": "4", "rotation": 90, "x": 3, "y": 4}, {"patternId": "7", "rotation": 90, "x": 3, "y": 3}, {"patternId": "3", "rotation": 180, "x": 3, "y": 2}, {"patternId": "I", "rotation": 90, "x": 3, "y": 1}, {"patternId": "I", "rotation": 180, "x": 2, "y": 1}, {"patternId": "3", "rotation": 90, "x": 2, "y": 2}], "slot_sequence": ["FRONT", "LEFT", "BACK", "LEFT", "FRONT", "BOTTOM", "BACK", "TOP", "LEFT", "BACK"], "required_slots": ["FRONT", "LEFT", "BACK", "BOTTOM", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "I", "rotation": 90}, "BOTTOM": {"patternId": "7", "rotation": 90}, "FRONT": {"patternId": "4", "rotation": 90}, "BACK": {"patternId": "3", "rotation": 180}, "LEFT": {"patternId": "I", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 90}, "BOTTOM": {"patternId": "7", "rotation": 90}, "FRONT": {"patternId": "4", "rotation": 90}, "BACK": {"patternId": "3", "rotation": 180}, "LEFT": {"patternId": "I", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C425\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> W -> E -> E -> N -> N -> N -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=4, rotation=90, flipVertical=true\n- step 2: patternId=I, rotation=90, flipVertical=true\n- step 3: patternId=3, rotation=0, flipVertical=true\n- step 4: patternId=I, rotation=90, flipVertical=true\n- step 5: patternId=4, rotation=90, flipVertical=true\n- step 6: patternId=7, rotation=90, flipVertical=true\n- step 7: patternId=3, rotation=180, flipVertical=true\n- step 8: patternId=I, rotation=90, flipVertical=true\n- step 9: patternId=I, rotation=180, flipVertical=true\n- step 10: patternId=3, rotation=90, flipVertical=true\n- allowed patternId values for this task: 4, I, 3, 7, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C425"} +{"sample_id": "C426", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> S -> S -> W -> S -> W -> S -> E -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "S", "S", "W", "S", "W", "S", "E", "S", "W"], "observed_path_faces": [{"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C426_path_sequence.png"}, "metadata": {"level_id": 426, "name": "Reconstruct 426", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-426.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["triangle", "F", "X", "star", "9", "heart"], "start_x": 3, "start_y": 2, "grid_width": 5, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "triangle", "rotation": 270}, "BOTTOM": {"patternId": "heart", "rotation": 90}, "FRONT": {"patternId": "F", "rotation": 270}, "BACK": {"patternId": "star", "rotation": 90}, "LEFT": {"patternId": "9", "rotation": 0}, "RIGHT": {"patternId": "X", "rotation": 90}}, "bottom_faces": [{"patternId": "heart", "rotation": 90, "x": 3, "y": 2}, {"patternId": "star", "rotation": 270, "x": 3, "y": 1}, {"patternId": "heart", "rotation": 90, "x": 3, "y": 2}, {"patternId": "F", "rotation": 270, "x": 3, "y": 3}, {"patternId": "9", "rotation": 0, "x": 2, "y": 3}, {"patternId": "triangle", "rotation": 180, "x": 2, "y": 4}, {"patternId": "star", "rotation": 180, "x": 1, "y": 4}, {"patternId": "X", "rotation": 180, "x": 1, "y": 5}, {"patternId": "triangle", "rotation": 90, "x": 2, "y": 5}, {"patternId": "F", "rotation": 90, "x": 2, "y": 6}, {"patternId": "X", "rotation": 270, "x": 1, "y": 6}], "slot_sequence": ["BACK", "BOTTOM", "FRONT", "LEFT", "TOP", "BACK", "RIGHT", "TOP", "FRONT", "RIGHT"], "required_slots": ["BACK", "BOTTOM", "FRONT", "LEFT", "TOP", "RIGHT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "triangle", "rotation": 270}, "BOTTOM": {"patternId": "heart", "rotation": 90}, "FRONT": {"patternId": "F", "rotation": 270}, "BACK": {"patternId": "star", "rotation": 270}, "LEFT": {"patternId": "9", "rotation": 90}, "RIGHT": {"patternId": "X", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "triangle", "rotation": 270}, "BOTTOM": {"patternId": "heart", "rotation": 90}, "FRONT": {"patternId": "F", "rotation": 270}, "BACK": {"patternId": "star", "rotation": 270}, "LEFT": {"patternId": "9", "rotation": 90}, "RIGHT": {"patternId": "X", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C426\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> S -> S -> W -> S -> W -> S -> E -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=star, rotation=270, flipVertical=true\n- step 2: patternId=heart, rotation=90, flipVertical=true\n- step 3: patternId=F, rotation=270, flipVertical=true\n- step 4: patternId=9, rotation=0, flipVertical=true\n- step 5: patternId=triangle, rotation=180, flipVertical=true\n- step 6: patternId=star, rotation=180, flipVertical=true\n- step 7: patternId=X, rotation=180, flipVertical=true\n- step 8: patternId=triangle, rotation=90, flipVertical=true\n- step 9: patternId=F, rotation=90, flipVertical=true\n- step 10: patternId=X, rotation=270, flipVertical=true\n- allowed patternId values for this task: star, heart, F, 9, triangle, X, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C426"} +{"sample_id": "C427", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> S -> E -> N -> E -> N -> N -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "S", "E", "N", "E", "N", "N", "E", "E"], "observed_path_faces": [{"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C427_path_sequence.png"}, "metadata": {"level_id": 427, "name": "Reconstruct 427", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-427.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["X", "star", "E", "X", "B", "D"], "start_x": 1, "start_y": 5, "grid_width": 7, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "X", "rotation": 90}, "BOTTOM": {"patternId": "D", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 0}, "BACK": {"patternId": "X", "rotation": 270}, "LEFT": {"patternId": "B", "rotation": 180}, "RIGHT": {"patternId": "E", "rotation": 180}}, "bottom_faces": [{"patternId": "D", "rotation": 0, "x": 1, "y": 5}, {"patternId": "X", "rotation": 90, "x": 1, "y": 4}, {"patternId": "X", "rotation": 90, "x": 1, "y": 3}, {"patternId": "X", "rotation": 90, "x": 1, "y": 4}, {"patternId": "E", "rotation": 0, "x": 2, "y": 4}, {"patternId": "X", "rotation": 0, "x": 2, "y": 3}, {"patternId": "star", "rotation": 270, "x": 3, "y": 3}, {"patternId": "B", "rotation": 90, "x": 3, "y": 2}, {"patternId": "X", "rotation": 180, "x": 3, "y": 1}, {"patternId": "D", "rotation": 90, "x": 4, "y": 1}, {"patternId": "star", "rotation": 90, "x": 5, "y": 1}], "slot_sequence": ["BACK", "TOP", "BACK", "RIGHT", "TOP", "FRONT", "LEFT", "BACK", "BOTTOM", "FRONT"], "required_slots": ["BACK", "TOP", "RIGHT", "FRONT", "LEFT", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "X", "rotation": 90}, "BOTTOM": {"patternId": "D", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 0}, "BACK": {"patternId": "X", "rotation": 90}, "LEFT": {"patternId": "B", "rotation": 270}, "RIGHT": {"patternId": "E", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "X", "rotation": 90}, "BOTTOM": {"patternId": "D", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 0}, "BACK": {"patternId": "X", "rotation": 90}, "LEFT": {"patternId": "B", "rotation": 270}, "RIGHT": {"patternId": "E", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C427\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> S -> E -> N -> E -> N -> N -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=X, rotation=90, flipVertical=true\n- step 2: patternId=X, rotation=90, flipVertical=true\n- step 3: patternId=X, rotation=90, flipVertical=true\n- step 4: patternId=E, rotation=0, flipVertical=true\n- step 5: patternId=X, rotation=0, flipVertical=true\n- step 6: patternId=star, rotation=270, flipVertical=true\n- step 7: patternId=B, rotation=90, flipVertical=true\n- step 8: patternId=X, rotation=180, flipVertical=true\n- step 9: patternId=D, rotation=90, flipVertical=true\n- step 10: patternId=star, rotation=90, flipVertical=true\n- allowed patternId values for this task: X, E, star, B, D, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C427"} +{"sample_id": "C428", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> N -> N -> E -> N -> E -> N -> N -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "N", "N", "E", "N", "E", "N", "N", "W", "W"], "observed_path_faces": [{"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C428_path_sequence.png"}, "metadata": {"level_id": 428, "name": "Reconstruct 428", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-428.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["star", "square", "A", "Q", "diamond", "R"], "start_x": 1, "start_y": 5, "grid_width": 5, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "star", "rotation": 180}, "BOTTOM": {"patternId": "R", "rotation": 90}, "FRONT": {"patternId": "square", "rotation": 270}, "BACK": {"patternId": "Q", "rotation": 90}, "LEFT": {"patternId": "diamond", "rotation": 270}, "RIGHT": {"patternId": "A", "rotation": 90}}, "bottom_faces": [{"patternId": "R", "rotation": 90, "x": 1, "y": 5}, {"patternId": "square", "rotation": 270, "x": 1, "y": 6}, {"patternId": "R", "rotation": 90, "x": 1, "y": 5}, {"patternId": "Q", "rotation": 270, "x": 1, "y": 4}, {"patternId": "A", "rotation": 270, "x": 2, "y": 4}, {"patternId": "star", "rotation": 90, "x": 2, "y": 3}, {"patternId": "square", "rotation": 180, "x": 3, "y": 3}, {"patternId": "diamond", "rotation": 180, "x": 3, "y": 2}, {"patternId": "Q", "rotation": 0, "x": 3, "y": 1}, {"patternId": "star", "rotation": 270, "x": 2, "y": 1}, {"patternId": "square", "rotation": 0, "x": 1, "y": 1}], "slot_sequence": ["FRONT", "BOTTOM", "BACK", "RIGHT", "TOP", "FRONT", "LEFT", "BACK", "TOP", "FRONT"], "required_slots": ["FRONT", "BOTTOM", "BACK", "RIGHT", "TOP", "LEFT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "star", "rotation": 180}, "BOTTOM": {"patternId": "R", "rotation": 90}, "FRONT": {"patternId": "square", "rotation": 270}, "BACK": {"patternId": "Q", "rotation": 270}, "LEFT": {"patternId": "diamond", "rotation": 0}, "RIGHT": {"patternId": "A", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 180}, "BOTTOM": {"patternId": "R", "rotation": 90}, "FRONT": {"patternId": "square", "rotation": 270}, "BACK": {"patternId": "Q", "rotation": 270}, "LEFT": {"patternId": "diamond", "rotation": 0}, "RIGHT": {"patternId": "A", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C428\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> N -> N -> E -> N -> E -> N -> N -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=square, rotation=270, flipVertical=true\n- step 2: patternId=R, rotation=90, flipVertical=true\n- step 3: patternId=Q, rotation=270, flipVertical=true\n- step 4: patternId=A, rotation=270, flipVertical=true\n- step 5: patternId=star, rotation=90, flipVertical=true\n- step 6: patternId=square, rotation=180, flipVertical=true\n- step 7: patternId=diamond, rotation=180, flipVertical=true\n- step 8: patternId=Q, rotation=0, flipVertical=true\n- step 9: patternId=star, rotation=270, flipVertical=true\n- step 10: patternId=square, rotation=0, flipVertical=true\n- allowed patternId values for this task: square, R, Q, A, star, diamond, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C428"} +{"sample_id": "C429", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> N -> W -> N -> N -> S -> N -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "N", "W", "N", "N", "S", "N", "S", "E"], "observed_path_faces": [{"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C429_path_sequence.png"}, "metadata": {"level_id": 429, "name": "Reconstruct 429", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-429.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["6", "P", "6", "E", "circle", "E"], "start_x": 3, "start_y": 5, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "6", "rotation": 270}, "BOTTOM": {"patternId": "E", "rotation": 0}, "FRONT": {"patternId": "P", "rotation": 90}, "BACK": {"patternId": "E", "rotation": 180}, "LEFT": {"patternId": "circle", "rotation": 270}, "RIGHT": {"patternId": "6", "rotation": 270}}, "bottom_faces": [{"patternId": "E", "rotation": 0, "x": 3, "y": 5}, {"patternId": "circle", "rotation": 180, "x": 2, "y": 5}, {"patternId": "E", "rotation": 90, "x": 2, "y": 4}, {"patternId": "6", "rotation": 180, "x": 2, "y": 3}, {"patternId": "6", "rotation": 270, "x": 1, "y": 3}, {"patternId": "P", "rotation": 90, "x": 1, "y": 2}, {"patternId": "E", "rotation": 0, "x": 1, "y": 1}, {"patternId": "P", "rotation": 90, "x": 1, "y": 2}, {"patternId": "E", "rotation": 0, "x": 1, "y": 1}, {"patternId": "P", "rotation": 90, "x": 1, "y": 2}, {"patternId": "6", "rotation": 270, "x": 2, "y": 2}], "slot_sequence": ["LEFT", "BACK", "RIGHT", "TOP", "FRONT", "BOTTOM", "FRONT", "BOTTOM", "FRONT", "RIGHT"], "required_slots": ["LEFT", "BACK", "RIGHT", "TOP", "FRONT", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "6", "rotation": 270}, "BOTTOM": {"patternId": "E", "rotation": 0}, "FRONT": {"patternId": "P", "rotation": 90}, "BACK": {"patternId": "E", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 270}, "BOTTOM": {"patternId": "E", "rotation": 0}, "FRONT": {"patternId": "P", "rotation": 90}, "BACK": {"patternId": "E", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C429\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> N -> W -> N -> N -> S -> N -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=circle, rotation=180, flipVertical=true\n- step 2: patternId=E, rotation=90, flipVertical=true\n- step 3: patternId=6, rotation=180, flipVertical=true\n- step 4: patternId=6, rotation=270, flipVertical=true\n- step 5: patternId=P, rotation=90, flipVertical=true\n- step 6: patternId=E, rotation=0, flipVertical=true\n- step 7: patternId=P, rotation=90, flipVertical=true\n- step 8: patternId=E, rotation=0, flipVertical=true\n- step 9: patternId=P, rotation=90, flipVertical=true\n- step 10: patternId=6, rotation=270, flipVertical=true\n- allowed patternId values for this task: circle, E, 6, P, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C429"} +{"sample_id": "C430", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> N -> N -> W -> S -> E -> N -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "N", "N", "W", "S", "E", "N", "W", "N"], "observed_path_faces": [{"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C430_path_sequence.png"}, "metadata": {"level_id": 430, "name": "Reconstruct 430", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-430.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["heart", "Y", "arrow_up", "9", "smile", "K"], "start_x": 4, "start_y": 4, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "heart", "rotation": 90}, "BOTTOM": {"patternId": "K", "rotation": 90}, "FRONT": {"patternId": "Y", "rotation": 0}, "BACK": {"patternId": "9", "rotation": 180}, "LEFT": {"patternId": "smile", "rotation": 0}, "RIGHT": {"patternId": "arrow_up", "rotation": 90}}, "bottom_faces": [{"patternId": "K", "rotation": 90, "x": 4, "y": 4}, {"patternId": "smile", "rotation": 270, "x": 3, "y": 4}, {"patternId": "heart", "rotation": 270, "x": 2, "y": 4}, {"patternId": "9", "rotation": 180, "x": 2, "y": 3}, {"patternId": "K", "rotation": 270, "x": 2, "y": 2}, {"patternId": "arrow_up", "rotation": 0, "x": 1, "y": 2}, {"patternId": "9", "rotation": 90, "x": 1, "y": 3}, {"patternId": "K", "rotation": 180, "x": 2, "y": 3}, {"patternId": "arrow_up", "rotation": 270, "x": 2, "y": 2}, {"patternId": "9", "rotation": 0, "x": 1, "y": 2}, {"patternId": "heart", "rotation": 90, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "TOP", "BACK", "BOTTOM", "RIGHT", "BACK", "BOTTOM", "RIGHT", "BACK", "TOP"], "required_slots": ["LEFT", "TOP", "BACK", "BOTTOM", "RIGHT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "heart", "rotation": 90}, "BOTTOM": {"patternId": "K", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "9", "rotation": 0}, "LEFT": {"patternId": "smile", "rotation": 90}, "RIGHT": {"patternId": "arrow_up", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "heart", "rotation": 90}, "BOTTOM": {"patternId": "K", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "9", "rotation": 0}, "LEFT": {"patternId": "smile", "rotation": 90}, "RIGHT": {"patternId": "arrow_up", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C430\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> N -> N -> W -> S -> E -> N -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=smile, rotation=270, flipVertical=true\n- step 2: patternId=heart, rotation=270, flipVertical=true\n- step 3: patternId=9, rotation=180, flipVertical=true\n- step 4: patternId=K, rotation=270, flipVertical=true\n- step 5: patternId=arrow_up, rotation=0, flipVertical=true\n- step 6: patternId=9, rotation=90, flipVertical=true\n- step 7: patternId=K, rotation=180, flipVertical=true\n- step 8: patternId=arrow_up, rotation=270, flipVertical=true\n- step 9: patternId=9, rotation=0, flipVertical=true\n- step 10: patternId=heart, rotation=90, flipVertical=true\n- allowed patternId values for this task: smile, heart, 9, K, arrow_up, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C430"} +{"sample_id": "C431", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> N -> W -> S -> S -> W -> W -> E -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "N", "W", "S", "S", "W", "W", "E", "E", "N"], "observed_path_faces": [{"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C431_path_sequence.png"}, "metadata": {"level_id": 431, "name": "Reconstruct 431", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-431.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["9", "arrow_left", "heart", "heart", "1", "O"], "start_x": 4, "start_y": 1, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "9", "rotation": 180}, "BOTTOM": {"patternId": "O", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 90}, "BACK": {"patternId": "heart", "rotation": 0}, "LEFT": {"patternId": "1", "rotation": 0}, "RIGHT": {"patternId": "heart", "rotation": 0}}, "bottom_faces": [{"patternId": "O", "rotation": 0, "x": 4, "y": 1}, {"patternId": "arrow_left", "rotation": 90, "x": 4, "y": 2}, {"patternId": "O", "rotation": 0, "x": 4, "y": 1}, {"patternId": "1", "rotation": 270, "x": 3, "y": 1}, {"patternId": "arrow_left", "rotation": 0, "x": 3, "y": 2}, {"patternId": "heart", "rotation": 270, "x": 3, "y": 3}, {"patternId": "9", "rotation": 180, "x": 2, "y": 3}, {"patternId": "1", "rotation": 90, "x": 1, "y": 3}, {"patternId": "9", "rotation": 180, "x": 2, "y": 3}, {"patternId": "heart", "rotation": 270, "x": 3, "y": 3}, {"patternId": "arrow_left", "rotation": 0, "x": 3, "y": 2}], "slot_sequence": ["FRONT", "BOTTOM", "LEFT", "FRONT", "RIGHT", "TOP", "LEFT", "TOP", "RIGHT", "FRONT"], "required_slots": ["FRONT", "BOTTOM", "LEFT", "RIGHT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "9", "rotation": 180}, "BOTTOM": {"patternId": "O", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "1", "rotation": 90}, "RIGHT": {"patternId": "heart", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "9", "rotation": 180}, "BOTTOM": {"patternId": "O", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "1", "rotation": 90}, "RIGHT": {"patternId": "heart", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C431\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> N -> W -> S -> S -> W -> W -> E -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_left, rotation=90, flipVertical=true\n- step 2: patternId=O, rotation=0, flipVertical=true\n- step 3: patternId=1, rotation=270, flipVertical=true\n- step 4: patternId=arrow_left, rotation=0, flipVertical=true\n- step 5: patternId=heart, rotation=270, flipVertical=true\n- step 6: patternId=9, rotation=180, flipVertical=true\n- step 7: patternId=1, rotation=90, flipVertical=true\n- step 8: patternId=9, rotation=180, flipVertical=true\n- step 9: patternId=heart, rotation=270, flipVertical=true\n- step 10: patternId=arrow_left, rotation=0, flipVertical=true\n- allowed patternId values for this task: arrow_left, O, 1, heart, 9, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C431"} +{"sample_id": "C432", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> W -> S -> W -> N -> S -> S -> S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "W", "S", "W", "N", "S", "S", "S", "N"], "observed_path_faces": [{"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C432_path_sequence.png"}, "metadata": {"level_id": 432, "name": "Reconstruct 432", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-432.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["9", "V", "star", "M", "4", "I"], "start_x": 4, "start_y": 2, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "9", "rotation": 270}, "BOTTOM": {"patternId": "I", "rotation": 0}, "FRONT": {"patternId": "V", "rotation": 180}, "BACK": {"patternId": "M", "rotation": 270}, "LEFT": {"patternId": "4", "rotation": 0}, "RIGHT": {"patternId": "star", "rotation": 0}}, "bottom_faces": [{"patternId": "I", "rotation": 0, "x": 4, "y": 2}, {"patternId": "4", "rotation": 270, "x": 3, "y": 2}, {"patternId": "M", "rotation": 180, "x": 3, "y": 1}, {"patternId": "9", "rotation": 0, "x": 2, "y": 1}, {"patternId": "4", "rotation": 180, "x": 2, "y": 2}, {"patternId": "V", "rotation": 0, "x": 1, "y": 2}, {"patternId": "9", "rotation": 90, "x": 1, "y": 1}, {"patternId": "V", "rotation": 0, "x": 1, "y": 2}, {"patternId": "I", "rotation": 180, "x": 1, "y": 3}, {"patternId": "M", "rotation": 270, "x": 1, "y": 4}, {"patternId": "I", "rotation": 180, "x": 1, "y": 3}], "slot_sequence": ["LEFT", "BACK", "TOP", "LEFT", "FRONT", "TOP", "FRONT", "BOTTOM", "BACK", "BOTTOM"], "required_slots": ["LEFT", "BACK", "TOP", "FRONT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "9", "rotation": 270}, "BOTTOM": {"patternId": "I", "rotation": 0}, "FRONT": {"patternId": "V", "rotation": 180}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "4", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "9", "rotation": 270}, "BOTTOM": {"patternId": "I", "rotation": 0}, "FRONT": {"patternId": "V", "rotation": 180}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "4", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C432\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> W -> S -> W -> N -> S -> S -> S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=4, rotation=270, flipVertical=true\n- step 2: patternId=M, rotation=180, flipVertical=true\n- step 3: patternId=9, rotation=0, flipVertical=true\n- step 4: patternId=4, rotation=180, flipVertical=true\n- step 5: patternId=V, rotation=0, flipVertical=true\n- step 6: patternId=9, rotation=90, flipVertical=true\n- step 7: patternId=V, rotation=0, flipVertical=true\n- step 8: patternId=I, rotation=180, flipVertical=true\n- step 9: patternId=M, rotation=270, flipVertical=true\n- step 10: patternId=I, rotation=180, flipVertical=true\n- allowed patternId values for this task: 4, M, 9, V, I, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C432"} +{"sample_id": "C433", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> N -> N -> E -> S -> E -> S -> W -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "N", "N", "E", "S", "E", "S", "W", "W", "N"], "observed_path_faces": [{"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C433_path_sequence.png"}, "metadata": {"level_id": 433, "name": "Reconstruct 433", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-433.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["T", "diamond", "arrow_up", "S", "1", "diamond"], "start_x": 1, "start_y": 2, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "T", "rotation": 180}, "BOTTOM": {"patternId": "diamond", "rotation": 90}, "FRONT": {"patternId": "diamond", "rotation": 180}, "BACK": {"patternId": "S", "rotation": 270}, "LEFT": {"patternId": "1", "rotation": 0}, "RIGHT": {"patternId": "arrow_up", "rotation": 270}}, "bottom_faces": [{"patternId": "diamond", "rotation": 90, "x": 1, "y": 2}, {"patternId": "diamond", "rotation": 180, "x": 1, "y": 3}, {"patternId": "diamond", "rotation": 90, "x": 1, "y": 2}, {"patternId": "S", "rotation": 90, "x": 1, "y": 1}, {"patternId": "arrow_up", "rotation": 90, "x": 2, "y": 1}, {"patternId": "diamond", "rotation": 180, "x": 2, "y": 2}, {"patternId": "diamond", "rotation": 270, "x": 3, "y": 2}, {"patternId": "1", "rotation": 90, "x": 3, "y": 3}, {"patternId": "diamond", "rotation": 270, "x": 2, "y": 3}, {"patternId": "arrow_up", "rotation": 180, "x": 1, "y": 3}, {"patternId": "diamond", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["FRONT", "BOTTOM", "BACK", "RIGHT", "BOTTOM", "FRONT", "LEFT", "BOTTOM", "RIGHT", "FRONT"], "required_slots": ["FRONT", "BOTTOM", "BACK", "RIGHT", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "diamond", "rotation": 90}, "FRONT": {"patternId": "diamond", "rotation": 180}, "BACK": {"patternId": "S", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 90}, "RIGHT": {"patternId": "arrow_up", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "diamond", "rotation": 90}, "FRONT": {"patternId": "diamond", "rotation": 180}, "BACK": {"patternId": "S", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 90}, "RIGHT": {"patternId": "arrow_up", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C433\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> N -> N -> E -> S -> E -> S -> W -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=diamond, rotation=180, flipVertical=true\n- step 2: patternId=diamond, rotation=90, flipVertical=true\n- step 3: patternId=S, rotation=90, flipVertical=true\n- step 4: patternId=arrow_up, rotation=90, flipVertical=true\n- step 5: patternId=diamond, rotation=180, flipVertical=true\n- step 6: patternId=diamond, rotation=270, flipVertical=true\n- step 7: patternId=1, rotation=90, flipVertical=true\n- step 8: patternId=diamond, rotation=270, flipVertical=true\n- step 9: patternId=arrow_up, rotation=180, flipVertical=true\n- step 10: patternId=diamond, rotation=90, flipVertical=true\n- allowed patternId values for this task: diamond, S, arrow_up, 1, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C433"} +{"sample_id": "C434", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> W -> N -> W -> S -> S -> W -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "W", "N", "W", "S", "S", "W", "W", "N"], "observed_path_faces": [{"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C434_path_sequence.png"}, "metadata": {"level_id": 434, "name": "Reconstruct 434", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-434.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["O", "heart", "L", "8", "N", "G"], "start_x": 4, "start_y": 3, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "G", "rotation": 270}, "FRONT": {"patternId": "heart", "rotation": 180}, "BACK": {"patternId": "8", "rotation": 90}, "LEFT": {"patternId": "N", "rotation": 180}, "RIGHT": {"patternId": "L", "rotation": 180}}, "bottom_faces": [{"patternId": "G", "rotation": 270, "x": 4, "y": 3}, {"patternId": "L", "rotation": 270, "x": 5, "y": 3}, {"patternId": "8", "rotation": 180, "x": 5, "y": 2}, {"patternId": "G", "rotation": 180, "x": 4, "y": 2}, {"patternId": "N", "rotation": 0, "x": 4, "y": 1}, {"patternId": "heart", "rotation": 0, "x": 3, "y": 1}, {"patternId": "G", "rotation": 90, "x": 3, "y": 2}, {"patternId": "8", "rotation": 90, "x": 3, "y": 3}, {"patternId": "L", "rotation": 180, "x": 2, "y": 3}, {"patternId": "heart", "rotation": 180, "x": 1, "y": 3}, {"patternId": "G", "rotation": 270, "x": 1, "y": 2}], "slot_sequence": ["RIGHT", "BACK", "BOTTOM", "LEFT", "FRONT", "BOTTOM", "BACK", "RIGHT", "FRONT", "BOTTOM"], "required_slots": ["RIGHT", "BACK", "BOTTOM", "LEFT", "FRONT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "G", "rotation": 270}, "FRONT": {"patternId": "heart", "rotation": 180}, "BACK": {"patternId": "8", "rotation": 270}, "LEFT": {"patternId": "N", "rotation": 270}, "RIGHT": {"patternId": "L", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "G", "rotation": 270}, "FRONT": {"patternId": "heart", "rotation": 180}, "BACK": {"patternId": "8", "rotation": 270}, "LEFT": {"patternId": "N", "rotation": 270}, "RIGHT": {"patternId": "L", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C434\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> W -> N -> W -> S -> S -> W -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=L, rotation=270, flipVertical=true\n- step 2: patternId=8, rotation=180, flipVertical=true\n- step 3: patternId=G, rotation=180, flipVertical=true\n- step 4: patternId=N, rotation=0, flipVertical=true\n- step 5: patternId=heart, rotation=0, flipVertical=true\n- step 6: patternId=G, rotation=90, flipVertical=true\n- step 7: patternId=8, rotation=90, flipVertical=true\n- step 8: patternId=L, rotation=180, flipVertical=true\n- step 9: patternId=heart, rotation=180, flipVertical=true\n- step 10: patternId=G, rotation=270, flipVertical=true\n- allowed patternId values for this task: L, 8, G, N, heart, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C434"} +{"sample_id": "C435", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> S -> E -> E -> S -> W -> E -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "S", "E", "E", "S", "W", "E", "W", "S"], "observed_path_faces": [{"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C435_path_sequence.png"}, "metadata": {"level_id": 435, "name": "Reconstruct 435", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-435.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["7", "star", "arrow_right", "star", "U", "B"], "start_x": 2, "start_y": 1, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "7", "rotation": 90}, "BOTTOM": {"patternId": "B", "rotation": 180}, "FRONT": {"patternId": "star", "rotation": 270}, "BACK": {"patternId": "star", "rotation": 270}, "LEFT": {"patternId": "U", "rotation": 90}, "RIGHT": {"patternId": "arrow_right", "rotation": 0}}, "bottom_faces": [{"patternId": "B", "rotation": 180, "x": 2, "y": 1}, {"patternId": "star", "rotation": 270, "x": 2, "y": 2}, {"patternId": "U", "rotation": 90, "x": 1, "y": 2}, {"patternId": "7", "rotation": 0, "x": 1, "y": 3}, {"patternId": "star", "rotation": 180, "x": 2, "y": 3}, {"patternId": "B", "rotation": 90, "x": 3, "y": 3}, {"patternId": "arrow_right", "rotation": 0, "x": 3, "y": 4}, {"patternId": "star", "rotation": 270, "x": 2, "y": 4}, {"patternId": "arrow_right", "rotation": 0, "x": 3, "y": 4}, {"patternId": "star", "rotation": 270, "x": 2, "y": 4}, {"patternId": "7", "rotation": 90, "x": 2, "y": 5}], "slot_sequence": ["FRONT", "LEFT", "TOP", "FRONT", "BOTTOM", "RIGHT", "FRONT", "RIGHT", "FRONT", "TOP"], "required_slots": ["FRONT", "LEFT", "TOP", "BOTTOM", "RIGHT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "7", "rotation": 90}, "BOTTOM": {"patternId": "B", "rotation": 180}, "FRONT": {"patternId": "star", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "U", "rotation": 180}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "7", "rotation": 90}, "BOTTOM": {"patternId": "B", "rotation": 180}, "FRONT": {"patternId": "star", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "U", "rotation": 180}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C435\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> S -> E -> E -> S -> W -> E -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=star, rotation=270, flipVertical=true\n- step 2: patternId=U, rotation=90, flipVertical=true\n- step 3: patternId=7, rotation=0, flipVertical=true\n- step 4: patternId=star, rotation=180, flipVertical=true\n- step 5: patternId=B, rotation=90, flipVertical=true\n- step 6: patternId=arrow_right, rotation=0, flipVertical=true\n- step 7: patternId=star, rotation=270, flipVertical=true\n- step 8: patternId=arrow_right, rotation=0, flipVertical=true\n- step 9: patternId=star, rotation=270, flipVertical=true\n- step 10: patternId=7, rotation=90, flipVertical=true\n- allowed patternId values for this task: star, U, 7, B, arrow_right, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C435"} +{"sample_id": "C436", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> E -> S -> S -> W -> N -> N -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "W", "E", "S", "S", "W", "N", "N", "S"], "observed_path_faces": [{"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C436_path_sequence.png"}, "metadata": {"level_id": 436, "name": "Reconstruct 436", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-436.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["8", "4", "E", "5", "heart", "3"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "8", "rotation": 0}, "BOTTOM": {"patternId": "3", "rotation": 0}, "FRONT": {"patternId": "4", "rotation": 180}, "BACK": {"patternId": "5", "rotation": 90}, "LEFT": {"patternId": "heart", "rotation": 0}, "RIGHT": {"patternId": "E", "rotation": 270}}, "bottom_faces": [{"patternId": "3", "rotation": 0, "x": 1, "y": 1}, {"patternId": "E", "rotation": 0, "x": 2, "y": 1}, {"patternId": "4", "rotation": 270, "x": 2, "y": 2}, {"patternId": "3", "rotation": 90, "x": 1, "y": 2}, {"patternId": "4", "rotation": 270, "x": 2, "y": 2}, {"patternId": "heart", "rotation": 90, "x": 2, "y": 3}, {"patternId": "5", "rotation": 180, "x": 2, "y": 4}, {"patternId": "3", "rotation": 270, "x": 1, "y": 4}, {"patternId": "heart", "rotation": 180, "x": 1, "y": 3}, {"patternId": "8", "rotation": 90, "x": 1, "y": 2}, {"patternId": "heart", "rotation": 180, "x": 1, "y": 3}], "slot_sequence": ["RIGHT", "FRONT", "BOTTOM", "FRONT", "LEFT", "BACK", "BOTTOM", "LEFT", "TOP", "LEFT"], "required_slots": ["RIGHT", "FRONT", "BOTTOM", "LEFT", "BACK", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "8", "rotation": 0}, "BOTTOM": {"patternId": "3", "rotation": 0}, "FRONT": {"patternId": "4", "rotation": 180}, "BACK": {"patternId": "5", "rotation": 270}, "LEFT": {"patternId": "heart", "rotation": 90}, "RIGHT": {"patternId": "E", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "8", "rotation": 0}, "BOTTOM": {"patternId": "3", "rotation": 0}, "FRONT": {"patternId": "4", "rotation": 180}, "BACK": {"patternId": "5", "rotation": 270}, "LEFT": {"patternId": "heart", "rotation": 90}, "RIGHT": {"patternId": "E", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C436\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> E -> S -> S -> W -> N -> N -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=E, rotation=0, flipVertical=true\n- step 2: patternId=4, rotation=270, flipVertical=true\n- step 3: patternId=3, rotation=90, flipVertical=true\n- step 4: patternId=4, rotation=270, flipVertical=true\n- step 5: patternId=heart, rotation=90, flipVertical=true\n- step 6: patternId=5, rotation=180, flipVertical=true\n- step 7: patternId=3, rotation=270, flipVertical=true\n- step 8: patternId=heart, rotation=180, flipVertical=true\n- step 9: patternId=8, rotation=90, flipVertical=true\n- step 10: patternId=heart, rotation=180, flipVertical=true\n- allowed patternId values for this task: E, 4, 3, heart, 5, 8, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C436"} +{"sample_id": "C437", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> W -> S -> S -> W -> W -> E -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "W", "S", "S", "W", "W", "E", "N", "N"], "observed_path_faces": [{"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C437_path_sequence.png"}, "metadata": {"level_id": 437, "name": "Reconstruct 437", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-437.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["5", "2", "smile", "N", "C", "U"], "start_x": 5, "start_y": 2, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "U", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "N", "rotation": 270}, "LEFT": {"patternId": "C", "rotation": 90}, "RIGHT": {"patternId": "smile", "rotation": 180}}, "bottom_faces": [{"patternId": "U", "rotation": 0, "x": 5, "y": 2}, {"patternId": "C", "rotation": 0, "x": 4, "y": 2}, {"patternId": "N", "rotation": 180, "x": 4, "y": 1}, {"patternId": "5", "rotation": 180, "x": 3, "y": 1}, {"patternId": "C", "rotation": 270, "x": 3, "y": 2}, {"patternId": "U", "rotation": 270, "x": 3, "y": 3}, {"patternId": "2", "rotation": 180, "x": 2, "y": 3}, {"patternId": "5", "rotation": 0, "x": 1, "y": 3}, {"patternId": "2", "rotation": 180, "x": 2, "y": 3}, {"patternId": "C", "rotation": 0, "x": 2, "y": 2}, {"patternId": "N", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["LEFT", "BACK", "TOP", "LEFT", "BOTTOM", "FRONT", "TOP", "FRONT", "LEFT", "BACK"], "required_slots": ["LEFT", "BACK", "TOP", "BOTTOM", "FRONT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "U", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "N", "rotation": 90}, "LEFT": {"patternId": "C", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "U", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "N", "rotation": 90}, "LEFT": {"patternId": "C", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C437\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> W -> S -> S -> W -> W -> E -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=C, rotation=0, flipVertical=true\n- step 2: patternId=N, rotation=180, flipVertical=true\n- step 3: patternId=5, rotation=180, flipVertical=true\n- step 4: patternId=C, rotation=270, flipVertical=true\n- step 5: patternId=U, rotation=270, flipVertical=true\n- step 6: patternId=2, rotation=180, flipVertical=true\n- step 7: patternId=5, rotation=0, flipVertical=true\n- step 8: patternId=2, rotation=180, flipVertical=true\n- step 9: patternId=C, rotation=0, flipVertical=true\n- step 10: patternId=N, rotation=180, flipVertical=true\n- allowed patternId values for this task: C, N, 5, U, 2, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C437"} +{"sample_id": "C438", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> E -> E -> S -> N -> S -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "W", "E", "E", "S", "N", "S", "E", "N"], "observed_path_faces": [{"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C438_path_sequence.png"}, "metadata": {"level_id": 438, "name": "Reconstruct 438", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-438.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["T", "L", "smile", "circle", "N", "F"], "start_x": 1, "start_y": 1, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "T", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 270}, "FRONT": {"patternId": "L", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 0}, "LEFT": {"patternId": "N", "rotation": 90}, "RIGHT": {"patternId": "smile", "rotation": 180}}, "bottom_faces": [{"patternId": "F", "rotation": 270, "x": 1, "y": 1}, {"patternId": "smile", "rotation": 270, "x": 2, "y": 1}, {"patternId": "L", "rotation": 90, "x": 2, "y": 2}, {"patternId": "F", "rotation": 0, "x": 1, "y": 2}, {"patternId": "L", "rotation": 90, "x": 2, "y": 2}, {"patternId": "T", "rotation": 90, "x": 3, "y": 2}, {"patternId": "N", "rotation": 270, "x": 3, "y": 3}, {"patternId": "T", "rotation": 90, "x": 3, "y": 2}, {"patternId": "N", "rotation": 270, "x": 3, "y": 3}, {"patternId": "circle", "rotation": 180, "x": 4, "y": 3}, {"patternId": "T", "rotation": 0, "x": 4, "y": 2}], "slot_sequence": ["RIGHT", "FRONT", "BOTTOM", "FRONT", "TOP", "LEFT", "TOP", "LEFT", "BACK", "TOP"], "required_slots": ["RIGHT", "FRONT", "BOTTOM", "TOP", "LEFT", "BACK"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "T", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 270}, "FRONT": {"patternId": "L", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 180}, "LEFT": {"patternId": "N", "rotation": 180}, "RIGHT": {"patternId": "smile", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "T", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 270}, "FRONT": {"patternId": "L", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 180}, "LEFT": {"patternId": "N", "rotation": 180}, "RIGHT": {"patternId": "smile", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C438\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> E -> E -> S -> N -> S -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=smile, rotation=270, flipVertical=true\n- step 2: patternId=L, rotation=90, flipVertical=true\n- step 3: patternId=F, rotation=0, flipVertical=true\n- step 4: patternId=L, rotation=90, flipVertical=true\n- step 5: patternId=T, rotation=90, flipVertical=true\n- step 6: patternId=N, rotation=270, flipVertical=true\n- step 7: patternId=T, rotation=90, flipVertical=true\n- step 8: patternId=N, rotation=270, flipVertical=true\n- step 9: patternId=circle, rotation=180, flipVertical=true\n- step 10: patternId=T, rotation=0, flipVertical=true\n- allowed patternId values for this task: smile, L, F, T, N, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C438"} +{"sample_id": "C439", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> W -> S -> N -> W -> W -> W -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "W", "S", "N", "W", "W", "W", "S", "E"], "observed_path_faces": [{"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C439_path_sequence.png"}, "metadata": {"level_id": 439, "name": "Reconstruct 439", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-439.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["5", "E", "X", "D", "arrow_right", "Z"], "start_x": 5, "start_y": 3, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "E", "rotation": 270}, "BACK": {"patternId": "D", "rotation": 180}, "LEFT": {"patternId": "arrow_right", "rotation": 0}, "RIGHT": {"patternId": "X", "rotation": 270}}, "bottom_faces": [{"patternId": "Z", "rotation": 270, "x": 5, "y": 3}, {"patternId": "D", "rotation": 0, "x": 5, "y": 2}, {"patternId": "5", "rotation": 90, "x": 5, "y": 1}, {"patternId": "arrow_right", "rotation": 90, "x": 4, "y": 1}, {"patternId": "D", "rotation": 270, "x": 4, "y": 2}, {"patternId": "arrow_right", "rotation": 90, "x": 4, "y": 1}, {"patternId": "Z", "rotation": 90, "x": 3, "y": 1}, {"patternId": "X", "rotation": 180, "x": 2, "y": 1}, {"patternId": "5", "rotation": 90, "x": 1, "y": 1}, {"patternId": "D", "rotation": 0, "x": 1, "y": 2}, {"patternId": "X", "rotation": 90, "x": 2, "y": 2}], "slot_sequence": ["BACK", "TOP", "LEFT", "BACK", "LEFT", "BOTTOM", "RIGHT", "TOP", "BACK", "RIGHT"], "required_slots": ["BACK", "TOP", "LEFT", "BOTTOM", "RIGHT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "arrow_right", "rotation": 90}, "RIGHT": {"patternId": "X", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "arrow_right", "rotation": 90}, "RIGHT": {"patternId": "X", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C439\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> W -> S -> N -> W -> W -> W -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=D, rotation=0, flipVertical=true\n- step 2: patternId=5, rotation=90, flipVertical=true\n- step 3: patternId=arrow_right, rotation=90, flipVertical=true\n- step 4: patternId=D, rotation=270, flipVertical=true\n- step 5: patternId=arrow_right, rotation=90, flipVertical=true\n- step 6: patternId=Z, rotation=90, flipVertical=true\n- step 7: patternId=X, rotation=180, flipVertical=true\n- step 8: patternId=5, rotation=90, flipVertical=true\n- step 9: patternId=D, rotation=0, flipVertical=true\n- step 10: patternId=X, rotation=90, flipVertical=true\n- allowed patternId values for this task: D, 5, arrow_right, Z, X, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C439"} +{"sample_id": "C440", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> E -> N -> E -> E -> S -> W -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "E", "N", "E", "E", "S", "W", "N", "N"], "observed_path_faces": [{"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C440_path_sequence.png"}, "metadata": {"level_id": 440, "name": "Reconstruct 440", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-440.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["T", "arrow_up", "A", "W", "star", "V"], "start_x": 1, "start_y": 4, "grid_width": 7, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "T", "rotation": 90}, "BOTTOM": {"patternId": "V", "rotation": 270}, "FRONT": {"patternId": "arrow_up", "rotation": 90}, "BACK": {"patternId": "W", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 270}, "RIGHT": {"patternId": "A", "rotation": 0}}, "bottom_faces": [{"patternId": "V", "rotation": 270, "x": 1, "y": 4}, {"patternId": "A", "rotation": 90, "x": 2, "y": 4}, {"patternId": "W", "rotation": 90, "x": 2, "y": 3}, {"patternId": "T", "rotation": 0, "x": 3, "y": 3}, {"patternId": "star", "rotation": 270, "x": 3, "y": 2}, {"patternId": "arrow_up", "rotation": 90, "x": 4, "y": 2}, {"patternId": "A", "rotation": 0, "x": 5, "y": 2}, {"patternId": "T", "rotation": 180, "x": 5, "y": 3}, {"patternId": "arrow_up", "rotation": 180, "x": 4, "y": 3}, {"patternId": "A", "rotation": 90, "x": 4, "y": 2}, {"patternId": "W", "rotation": 90, "x": 4, "y": 1}], "slot_sequence": ["RIGHT", "BACK", "TOP", "LEFT", "FRONT", "RIGHT", "TOP", "FRONT", "RIGHT", "BACK"], "required_slots": ["RIGHT", "BACK", "TOP", "LEFT", "FRONT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "T", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_up", "rotation": 90}, "BACK": {"patternId": "W", "rotation": 180}, "LEFT": {"patternId": "star", "rotation": 0}, "RIGHT": {"patternId": "A", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "T", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_up", "rotation": 90}, "BACK": {"patternId": "W", "rotation": 180}, "LEFT": {"patternId": "star", "rotation": 0}, "RIGHT": {"patternId": "A", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C440\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> E -> N -> E -> E -> S -> W -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=A, rotation=90, flipVertical=true\n- step 2: patternId=W, rotation=90, flipVertical=true\n- step 3: patternId=T, rotation=0, flipVertical=true\n- step 4: patternId=star, rotation=270, flipVertical=true\n- step 5: patternId=arrow_up, rotation=90, flipVertical=true\n- step 6: patternId=A, rotation=0, flipVertical=true\n- step 7: patternId=T, rotation=180, flipVertical=true\n- step 8: patternId=arrow_up, rotation=180, flipVertical=true\n- step 9: patternId=A, rotation=90, flipVertical=true\n- step 10: patternId=W, rotation=90, flipVertical=true\n- allowed patternId values for this task: A, W, T, star, arrow_up, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C440"} +{"sample_id": "C441", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> S -> S -> N -> E -> W -> W -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "S", "S", "N", "E", "W", "W", "S", "S"], "observed_path_faces": [{"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C441_path_sequence.png"}, "metadata": {"level_id": 441, "name": "Reconstruct 441", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-441.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_up", "B", "V", "F", "Z", "arrow_left"], "start_x": 1, "start_y": 1, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "arrow_up", "rotation": 0}, "BOTTOM": {"patternId": "arrow_left", "rotation": 270}, "FRONT": {"patternId": "B", "rotation": 0}, "BACK": {"patternId": "F", "rotation": 0}, "LEFT": {"patternId": "Z", "rotation": 90}, "RIGHT": {"patternId": "V", "rotation": 90}}, "bottom_faces": [{"patternId": "arrow_left", "rotation": 270, "x": 1, "y": 1}, {"patternId": "V", "rotation": 180, "x": 2, "y": 1}, {"patternId": "arrow_up", "rotation": 180, "x": 3, "y": 1}, {"patternId": "B", "rotation": 180, "x": 3, "y": 2}, {"patternId": "arrow_left", "rotation": 90, "x": 3, "y": 3}, {"patternId": "B", "rotation": 180, "x": 3, "y": 2}, {"patternId": "Z", "rotation": 270, "x": 4, "y": 2}, {"patternId": "B", "rotation": 180, "x": 3, "y": 2}, {"patternId": "V", "rotation": 270, "x": 2, "y": 2}, {"patternId": "arrow_left", "rotation": 0, "x": 2, "y": 3}, {"patternId": "Z", "rotation": 90, "x": 2, "y": 4}], "slot_sequence": ["RIGHT", "TOP", "FRONT", "BOTTOM", "FRONT", "LEFT", "FRONT", "RIGHT", "BOTTOM", "LEFT"], "required_slots": ["RIGHT", "TOP", "FRONT", "BOTTOM", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "arrow_up", "rotation": 0}, "BOTTOM": {"patternId": "arrow_left", "rotation": 270}, "FRONT": {"patternId": "B", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Z", "rotation": 180}, "RIGHT": {"patternId": "V", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "arrow_up", "rotation": 0}, "BOTTOM": {"patternId": "arrow_left", "rotation": 270}, "FRONT": {"patternId": "B", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Z", "rotation": 180}, "RIGHT": {"patternId": "V", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C441\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> S -> S -> N -> E -> W -> W -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=V, rotation=180, flipVertical=true\n- step 2: patternId=arrow_up, rotation=180, flipVertical=true\n- step 3: patternId=B, rotation=180, flipVertical=true\n- step 4: patternId=arrow_left, rotation=90, flipVertical=true\n- step 5: patternId=B, rotation=180, flipVertical=true\n- step 6: patternId=Z, rotation=270, flipVertical=true\n- step 7: patternId=B, rotation=180, flipVertical=true\n- step 8: patternId=V, rotation=270, flipVertical=true\n- step 9: patternId=arrow_left, rotation=0, flipVertical=true\n- step 10: patternId=Z, rotation=90, flipVertical=true\n- allowed patternId values for this task: V, arrow_up, B, arrow_left, Z, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C441"} +{"sample_id": "C442", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> W -> N -> E -> N -> E -> N -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "W", "N", "E", "N", "E", "N", "W", "N"], "observed_path_faces": [{"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C442_path_sequence.png"}, "metadata": {"level_id": 442, "name": "Reconstruct 442", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-442.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["5", "diamond", "5", "L", "5", "arrow_left"], "start_x": 3, "start_y": 6, "grid_width": 5, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 90}, "BACK": {"patternId": "L", "rotation": 270}, "LEFT": {"patternId": "5", "rotation": 0}, "RIGHT": {"patternId": "5", "rotation": 180}}, "bottom_faces": [{"patternId": "arrow_left", "rotation": 0, "x": 3, "y": 6}, {"patternId": "5", "rotation": 270, "x": 2, "y": 6}, {"patternId": "L", "rotation": 180, "x": 2, "y": 5}, {"patternId": "5", "rotation": 180, "x": 1, "y": 5}, {"patternId": "5", "rotation": 180, "x": 1, "y": 4}, {"patternId": "L", "rotation": 270, "x": 2, "y": 4}, {"patternId": "arrow_left", "rotation": 180, "x": 2, "y": 3}, {"patternId": "5", "rotation": 90, "x": 3, "y": 3}, {"patternId": "diamond", "rotation": 180, "x": 3, "y": 2}, {"patternId": "arrow_left", "rotation": 90, "x": 2, "y": 2}, {"patternId": "5", "rotation": 0, "x": 2, "y": 1}], "slot_sequence": ["LEFT", "BACK", "TOP", "RIGHT", "BACK", "BOTTOM", "LEFT", "FRONT", "BOTTOM", "RIGHT"], "required_slots": ["LEFT", "BACK", "TOP", "RIGHT", "BOTTOM", "FRONT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 90}, "BACK": {"patternId": "L", "rotation": 90}, "LEFT": {"patternId": "5", "rotation": 90}, "RIGHT": {"patternId": "5", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 90}, "BACK": {"patternId": "L", "rotation": 90}, "LEFT": {"patternId": "5", "rotation": 90}, "RIGHT": {"patternId": "5", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C442\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> W -> N -> E -> N -> E -> N -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=5, rotation=270, flipVertical=true\n- step 2: patternId=L, rotation=180, flipVertical=true\n- step 3: patternId=5, rotation=180, flipVertical=true\n- step 4: patternId=5, rotation=180, flipVertical=true\n- step 5: patternId=L, rotation=270, flipVertical=true\n- step 6: patternId=arrow_left, rotation=180, flipVertical=true\n- step 7: patternId=5, rotation=90, flipVertical=true\n- step 8: patternId=diamond, rotation=180, flipVertical=true\n- step 9: patternId=arrow_left, rotation=90, flipVertical=true\n- step 10: patternId=5, rotation=0, flipVertical=true\n- allowed patternId values for this task: 5, L, arrow_left, diamond, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C442"} +{"sample_id": "C443", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> S -> S -> N -> E -> N -> W -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "S", "S", "N", "E", "N", "W", "N", "E"], "observed_path_faces": [{"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C443_path_sequence.png"}, "metadata": {"level_id": 443, "name": "Reconstruct 443", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-443.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["P", "K", "G", "heart", "circle", "9"], "start_x": 1, "start_y": 2, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "P", "rotation": 270}, "BOTTOM": {"patternId": "9", "rotation": 270}, "FRONT": {"patternId": "K", "rotation": 270}, "BACK": {"patternId": "heart", "rotation": 270}, "LEFT": {"patternId": "circle", "rotation": 90}, "RIGHT": {"patternId": "G", "rotation": 90}}, "bottom_faces": [{"patternId": "9", "rotation": 270, "x": 1, "y": 2}, {"patternId": "G", "rotation": 180, "x": 2, "y": 2}, {"patternId": "P", "rotation": 90, "x": 3, "y": 2}, {"patternId": "K", "rotation": 90, "x": 3, "y": 3}, {"patternId": "9", "rotation": 90, "x": 3, "y": 4}, {"patternId": "K", "rotation": 90, "x": 3, "y": 3}, {"patternId": "circle", "rotation": 270, "x": 4, "y": 3}, {"patternId": "P", "rotation": 0, "x": 4, "y": 2}, {"patternId": "K", "rotation": 0, "x": 3, "y": 2}, {"patternId": "G", "rotation": 180, "x": 3, "y": 1}, {"patternId": "P", "rotation": 90, "x": 4, "y": 1}], "slot_sequence": ["RIGHT", "TOP", "FRONT", "BOTTOM", "FRONT", "LEFT", "TOP", "FRONT", "RIGHT", "TOP"], "required_slots": ["RIGHT", "TOP", "FRONT", "BOTTOM", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "P", "rotation": 270}, "BOTTOM": {"patternId": "9", "rotation": 270}, "FRONT": {"patternId": "K", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 180}, "RIGHT": {"patternId": "G", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "P", "rotation": 270}, "BOTTOM": {"patternId": "9", "rotation": 270}, "FRONT": {"patternId": "K", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 180}, "RIGHT": {"patternId": "G", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C443\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> S -> S -> N -> E -> N -> W -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=G, rotation=180, flipVertical=true\n- step 2: patternId=P, rotation=90, flipVertical=true\n- step 3: patternId=K, rotation=90, flipVertical=true\n- step 4: patternId=9, rotation=90, flipVertical=true\n- step 5: patternId=K, rotation=90, flipVertical=true\n- step 6: patternId=circle, rotation=270, flipVertical=true\n- step 7: patternId=P, rotation=0, flipVertical=true\n- step 8: patternId=K, rotation=0, flipVertical=true\n- step 9: patternId=G, rotation=180, flipVertical=true\n- step 10: patternId=P, rotation=90, flipVertical=true\n- allowed patternId values for this task: G, P, K, 9, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C443"} +{"sample_id": "C444", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> W -> E -> S -> S -> N -> E -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "W", "E", "S", "S", "N", "E", "E", "E"], "observed_path_faces": [{"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C444_path_sequence.png"}, "metadata": {"level_id": 444, "name": "Reconstruct 444", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-444.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Z", "arrow_right", "D", "8", "1", "arrow_left"], "start_x": 3, "start_y": 1, "grid_width": 7, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "Z", "rotation": 180}, "BOTTOM": {"patternId": "arrow_left", "rotation": 90}, "FRONT": {"patternId": "arrow_right", "rotation": 180}, "BACK": {"patternId": "8", "rotation": 180}, "LEFT": {"patternId": "1", "rotation": 90}, "RIGHT": {"patternId": "D", "rotation": 180}}, "bottom_faces": [{"patternId": "arrow_left", "rotation": 90, "x": 3, "y": 1}, {"patternId": "arrow_right", "rotation": 180, "x": 3, "y": 2}, {"patternId": "1", "rotation": 90, "x": 2, "y": 2}, {"patternId": "8", "rotation": 180, "x": 1, "y": 2}, {"patternId": "1", "rotation": 90, "x": 2, "y": 2}, {"patternId": "Z", "rotation": 90, "x": 2, "y": 3}, {"patternId": "D", "rotation": 0, "x": 2, "y": 4}, {"patternId": "Z", "rotation": 90, "x": 2, "y": 3}, {"patternId": "arrow_right", "rotation": 90, "x": 3, "y": 3}, {"patternId": "arrow_left", "rotation": 0, "x": 4, "y": 3}, {"patternId": "8", "rotation": 270, "x": 5, "y": 3}], "slot_sequence": ["FRONT", "LEFT", "BACK", "LEFT", "TOP", "RIGHT", "TOP", "FRONT", "BOTTOM", "BACK"], "required_slots": ["FRONT", "LEFT", "BACK", "TOP", "RIGHT", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "Z", "rotation": 180}, "BOTTOM": {"patternId": "arrow_left", "rotation": 90}, "FRONT": {"patternId": "arrow_right", "rotation": 180}, "BACK": {"patternId": "8", "rotation": 0}, "LEFT": {"patternId": "1", "rotation": 180}, "RIGHT": {"patternId": "D", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "Z", "rotation": 180}, "BOTTOM": {"patternId": "arrow_left", "rotation": 90}, "FRONT": {"patternId": "arrow_right", "rotation": 180}, "BACK": {"patternId": "8", "rotation": 0}, "LEFT": {"patternId": "1", "rotation": 180}, "RIGHT": {"patternId": "D", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C444\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> W -> E -> S -> S -> N -> E -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_right, rotation=180, flipVertical=true\n- step 2: patternId=1, rotation=90, flipVertical=true\n- step 3: patternId=8, rotation=180, flipVertical=true\n- step 4: patternId=1, rotation=90, flipVertical=true\n- step 5: patternId=Z, rotation=90, flipVertical=true\n- step 6: patternId=D, rotation=0, flipVertical=true\n- step 7: patternId=Z, rotation=90, flipVertical=true\n- step 8: patternId=arrow_right, rotation=90, flipVertical=true\n- step 9: patternId=arrow_left, rotation=0, flipVertical=true\n- step 10: patternId=8, rotation=270, flipVertical=true\n- allowed patternId values for this task: arrow_right, 1, 8, Z, D, arrow_left, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C444"} +{"sample_id": "C445", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> E -> W -> W -> W -> S -> S -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "E", "W", "W", "W", "S", "S", "W", "S"], "observed_path_faces": [{"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C445_path_sequence.png"}, "metadata": {"level_id": 445, "name": "Reconstruct 445", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-445.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Q", "F", "R", "smile", "plus", "B"], "start_x": 4, "start_y": 1, "grid_width": 7, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "Q", "rotation": 0}, "BOTTOM": {"patternId": "B", "rotation": 0}, "FRONT": {"patternId": "F", "rotation": 90}, "BACK": {"patternId": "smile", "rotation": 270}, "LEFT": {"patternId": "plus", "rotation": 90}, "RIGHT": {"patternId": "R", "rotation": 90}}, "bottom_faces": [{"patternId": "B", "rotation": 0, "x": 4, "y": 1}, {"patternId": "F", "rotation": 90, "x": 4, "y": 2}, {"patternId": "Q", "rotation": 0, "x": 4, "y": 3}, {"patternId": "R", "rotation": 0, "x": 5, "y": 3}, {"patternId": "Q", "rotation": 0, "x": 4, "y": 3}, {"patternId": "plus", "rotation": 180, "x": 3, "y": 3}, {"patternId": "B", "rotation": 180, "x": 2, "y": 3}, {"patternId": "smile", "rotation": 270, "x": 2, "y": 4}, {"patternId": "Q", "rotation": 180, "x": 2, "y": 5}, {"patternId": "R", "rotation": 180, "x": 1, "y": 5}, {"patternId": "F", "rotation": 180, "x": 1, "y": 6}], "slot_sequence": ["FRONT", "TOP", "RIGHT", "TOP", "LEFT", "BOTTOM", "BACK", "TOP", "RIGHT", "FRONT"], "required_slots": ["FRONT", "TOP", "RIGHT", "LEFT", "BOTTOM", "BACK"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "Q", "rotation": 0}, "BOTTOM": {"patternId": "B", "rotation": 0}, "FRONT": {"patternId": "F", "rotation": 90}, "BACK": {"patternId": "smile", "rotation": 90}, "LEFT": {"patternId": "plus", "rotation": 180}, "RIGHT": {"patternId": "R", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "Q", "rotation": 0}, "BOTTOM": {"patternId": "B", "rotation": 0}, "FRONT": {"patternId": "F", "rotation": 90}, "BACK": {"patternId": "smile", "rotation": 90}, "LEFT": {"patternId": "plus", "rotation": 180}, "RIGHT": {"patternId": "R", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C445\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> E -> W -> W -> W -> S -> S -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=F, rotation=90, flipVertical=true\n- step 2: patternId=Q, rotation=0, flipVertical=true\n- step 3: patternId=R, rotation=0, flipVertical=true\n- step 4: patternId=Q, rotation=0, flipVertical=true\n- step 5: patternId=plus, rotation=180, flipVertical=true\n- step 6: patternId=B, rotation=180, flipVertical=true\n- step 7: patternId=smile, rotation=270, flipVertical=true\n- step 8: patternId=Q, rotation=180, flipVertical=true\n- step 9: patternId=R, rotation=180, flipVertical=true\n- step 10: patternId=F, rotation=180, flipVertical=true\n- allowed patternId values for this task: F, Q, R, plus, B, smile, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C445"} +{"sample_id": "C446", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> S -> S -> W -> S -> S -> E -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "S", "S", "W", "S", "S", "E", "N", "W"], "observed_path_faces": [{"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C446_path_sequence.png"}, "metadata": {"level_id": 446, "name": "Reconstruct 446", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-446.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["M", "triangle", "R", "3", "arrow_right", "diamond"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "M", "rotation": 270}, "BOTTOM": {"patternId": "diamond", "rotation": 90}, "FRONT": {"patternId": "triangle", "rotation": 270}, "BACK": {"patternId": "3", "rotation": 90}, "LEFT": {"patternId": "arrow_right", "rotation": 180}, "RIGHT": {"patternId": "R", "rotation": 180}}, "bottom_faces": [{"patternId": "diamond", "rotation": 90, "x": 3, "y": 1}, {"patternId": "triangle", "rotation": 270, "x": 3, "y": 2}, {"patternId": "arrow_right", "rotation": 180, "x": 2, "y": 2}, {"patternId": "M", "rotation": 180, "x": 2, "y": 3}, {"patternId": "R", "rotation": 0, "x": 2, "y": 4}, {"patternId": "3", "rotation": 270, "x": 1, "y": 4}, {"patternId": "diamond", "rotation": 90, "x": 1, "y": 5}, {"patternId": "triangle", "rotation": 270, "x": 1, "y": 6}, {"patternId": "R", "rotation": 180, "x": 2, "y": 6}, {"patternId": "diamond", "rotation": 0, "x": 2, "y": 5}, {"patternId": "triangle", "rotation": 180, "x": 1, "y": 5}], "slot_sequence": ["FRONT", "LEFT", "TOP", "RIGHT", "BACK", "BOTTOM", "FRONT", "RIGHT", "BOTTOM", "FRONT"], "required_slots": ["FRONT", "LEFT", "TOP", "RIGHT", "BACK", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "M", "rotation": 270}, "BOTTOM": {"patternId": "diamond", "rotation": 90}, "FRONT": {"patternId": "triangle", "rotation": 270}, "BACK": {"patternId": "3", "rotation": 270}, "LEFT": {"patternId": "arrow_right", "rotation": 270}, "RIGHT": {"patternId": "R", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 270}, "BOTTOM": {"patternId": "diamond", "rotation": 90}, "FRONT": {"patternId": "triangle", "rotation": 270}, "BACK": {"patternId": "3", "rotation": 270}, "LEFT": {"patternId": "arrow_right", "rotation": 270}, "RIGHT": {"patternId": "R", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C446\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> S -> S -> W -> S -> S -> E -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=triangle, rotation=270, flipVertical=true\n- step 2: patternId=arrow_right, rotation=180, flipVertical=true\n- step 3: patternId=M, rotation=180, flipVertical=true\n- step 4: patternId=R, rotation=0, flipVertical=true\n- step 5: patternId=3, rotation=270, flipVertical=true\n- step 6: patternId=diamond, rotation=90, flipVertical=true\n- step 7: patternId=triangle, rotation=270, flipVertical=true\n- step 8: patternId=R, rotation=180, flipVertical=true\n- step 9: patternId=diamond, rotation=0, flipVertical=true\n- step 10: patternId=triangle, rotation=180, flipVertical=true\n- allowed patternId values for this task: triangle, arrow_right, M, R, 3, diamond, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C446"} +{"sample_id": "C447", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> E -> N -> S -> W -> W -> N -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "E", "N", "S", "W", "W", "N", "W", "W"], "observed_path_faces": [{"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C447_path_sequence.png"}, "metadata": {"level_id": 447, "name": "Reconstruct 447", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-447.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["smile", "W", "L", "arrow_left", "Y", "arrow_up"], "start_x": 3, "start_y": 1, "grid_width": 7, "grid_height": 4, "true_solution_faces": {"TOP": {"patternId": "smile", "rotation": 90}, "BOTTOM": {"patternId": "arrow_up", "rotation": 180}, "FRONT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "arrow_left", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 90}, "RIGHT": {"patternId": "L", "rotation": 180}}, "bottom_faces": [{"patternId": "arrow_up", "rotation": 180, "x": 3, "y": 1}, {"patternId": "W", "rotation": 90, "x": 3, "y": 2}, {"patternId": "L", "rotation": 180, "x": 4, "y": 2}, {"patternId": "arrow_left", "rotation": 0, "x": 5, "y": 2}, {"patternId": "arrow_up", "rotation": 0, "x": 5, "y": 1}, {"patternId": "arrow_left", "rotation": 0, "x": 5, "y": 2}, {"patternId": "L", "rotation": 180, "x": 4, "y": 2}, {"patternId": "W", "rotation": 90, "x": 3, "y": 2}, {"patternId": "arrow_up", "rotation": 180, "x": 3, "y": 1}, {"patternId": "Y", "rotation": 0, "x": 2, "y": 1}, {"patternId": "smile", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["FRONT", "RIGHT", "BACK", "BOTTOM", "BACK", "RIGHT", "FRONT", "BOTTOM", "LEFT", "TOP"], "required_slots": ["FRONT", "RIGHT", "BACK", "BOTTOM", "LEFT", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "smile", "rotation": 90}, "BOTTOM": {"patternId": "arrow_up", "rotation": 180}, "FRONT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "arrow_left", "rotation": 180}, "LEFT": {"patternId": "Y", "rotation": 180}, "RIGHT": {"patternId": "L", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 90}, "BOTTOM": {"patternId": "arrow_up", "rotation": 180}, "FRONT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "arrow_left", "rotation": 180}, "LEFT": {"patternId": "Y", "rotation": 180}, "RIGHT": {"patternId": "L", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C447\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> E -> N -> S -> W -> W -> N -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=W, rotation=90, flipVertical=true\n- step 2: patternId=L, rotation=180, flipVertical=true\n- step 3: patternId=arrow_left, rotation=0, flipVertical=true\n- step 4: patternId=arrow_up, rotation=0, flipVertical=true\n- step 5: patternId=arrow_left, rotation=0, flipVertical=true\n- step 6: patternId=L, rotation=180, flipVertical=true\n- step 7: patternId=W, rotation=90, flipVertical=true\n- step 8: patternId=arrow_up, rotation=180, flipVertical=true\n- step 9: patternId=Y, rotation=0, flipVertical=true\n- step 10: patternId=smile, rotation=270, flipVertical=true\n- allowed patternId values for this task: W, L, arrow_left, arrow_up, Y, smile, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C447"} +{"sample_id": "C448", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> E -> S -> N -> E -> E -> S -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "E", "S", "N", "E", "E", "S", "W", "S"], "observed_path_faces": [{"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C448_path_sequence.png"}, "metadata": {"level_id": 448, "name": "Reconstruct 448", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-448.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["circle", "arrow_left", "X", "6", "4", "I"], "start_x": 2, "start_y": 1, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "circle", "rotation": 0}, "BOTTOM": {"patternId": "I", "rotation": 270}, "FRONT": {"patternId": "arrow_left", "rotation": 0}, "BACK": {"patternId": "6", "rotation": 180}, "LEFT": {"patternId": "4", "rotation": 180}, "RIGHT": {"patternId": "X", "rotation": 180}}, "bottom_faces": [{"patternId": "I", "rotation": 270, "x": 2, "y": 1}, {"patternId": "4", "rotation": 90, "x": 1, "y": 1}, {"patternId": "arrow_left", "rotation": 270, "x": 1, "y": 2}, {"patternId": "I", "rotation": 180, "x": 2, "y": 2}, {"patternId": "X", "rotation": 180, "x": 2, "y": 3}, {"patternId": "I", "rotation": 180, "x": 2, "y": 2}, {"patternId": "6", "rotation": 270, "x": 3, "y": 2}, {"patternId": "circle", "rotation": 270, "x": 4, "y": 2}, {"patternId": "X", "rotation": 0, "x": 4, "y": 3}, {"patternId": "6", "rotation": 0, "x": 3, "y": 3}, {"patternId": "I", "rotation": 270, "x": 3, "y": 4}], "slot_sequence": ["LEFT", "FRONT", "BOTTOM", "RIGHT", "BOTTOM", "BACK", "TOP", "RIGHT", "BACK", "BOTTOM"], "required_slots": ["LEFT", "FRONT", "BOTTOM", "RIGHT", "BACK", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "circle", "rotation": 0}, "BOTTOM": {"patternId": "I", "rotation": 270}, "FRONT": {"patternId": "arrow_left", "rotation": 0}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "4", "rotation": 270}, "RIGHT": {"patternId": "X", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 0}, "BOTTOM": {"patternId": "I", "rotation": 270}, "FRONT": {"patternId": "arrow_left", "rotation": 0}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "4", "rotation": 270}, "RIGHT": {"patternId": "X", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C448\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> E -> S -> N -> E -> E -> S -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=4, rotation=90, flipVertical=true\n- step 2: patternId=arrow_left, rotation=270, flipVertical=true\n- step 3: patternId=I, rotation=180, flipVertical=true\n- step 4: patternId=X, rotation=180, flipVertical=true\n- step 5: patternId=I, rotation=180, flipVertical=true\n- step 6: patternId=6, rotation=270, flipVertical=true\n- step 7: patternId=circle, rotation=270, flipVertical=true\n- step 8: patternId=X, rotation=0, flipVertical=true\n- step 9: patternId=6, rotation=0, flipVertical=true\n- step 10: patternId=I, rotation=270, flipVertical=true\n- allowed patternId values for this task: 4, arrow_left, I, X, 6, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C448"} +{"sample_id": "C449", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> W -> E -> E -> S -> W -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "W", "W", "E", "E", "S", "W", "N", "E"], "observed_path_faces": [{"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C449_path_sequence.png"}, "metadata": {"level_id": 449, "name": "Reconstruct 449", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-449.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["D", "square", "star", "smile", "smile", "N"], "start_x": 2, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "D", "rotation": 90}, "BOTTOM": {"patternId": "N", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 0}, "BACK": {"patternId": "smile", "rotation": 90}, "LEFT": {"patternId": "smile", "rotation": 180}, "RIGHT": {"patternId": "star", "rotation": 0}}, "bottom_faces": [{"patternId": "N", "rotation": 0, "x": 2, "y": 1}, {"patternId": "star", "rotation": 90, "x": 3, "y": 1}, {"patternId": "square", "rotation": 90, "x": 3, "y": 2}, {"patternId": "N", "rotation": 90, "x": 2, "y": 2}, {"patternId": "smile", "rotation": 0, "x": 1, "y": 2}, {"patternId": "N", "rotation": 90, "x": 2, "y": 2}, {"patternId": "square", "rotation": 90, "x": 3, "y": 2}, {"patternId": "smile", "rotation": 270, "x": 3, "y": 3}, {"patternId": "N", "rotation": 180, "x": 2, "y": 3}, {"patternId": "square", "rotation": 180, "x": 2, "y": 2}, {"patternId": "smile", "rotation": 0, "x": 3, "y": 2}], "slot_sequence": ["RIGHT", "FRONT", "BOTTOM", "BACK", "BOTTOM", "FRONT", "LEFT", "BOTTOM", "FRONT", "LEFT"], "required_slots": ["RIGHT", "FRONT", "BOTTOM", "BACK", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "N", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 0}, "BACK": {"patternId": "smile", "rotation": 270}, "LEFT": {"patternId": "smile", "rotation": 270}, "RIGHT": {"patternId": "star", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "N", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 0}, "BACK": {"patternId": "smile", "rotation": 270}, "LEFT": {"patternId": "smile", "rotation": 270}, "RIGHT": {"patternId": "star", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C449\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> W -> E -> E -> S -> W -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=star, rotation=90, flipVertical=true\n- step 2: patternId=square, rotation=90, flipVertical=true\n- step 3: patternId=N, rotation=90, flipVertical=true\n- step 4: patternId=smile, rotation=0, flipVertical=true\n- step 5: patternId=N, rotation=90, flipVertical=true\n- step 6: patternId=square, rotation=90, flipVertical=true\n- step 7: patternId=smile, rotation=270, flipVertical=true\n- step 8: patternId=N, rotation=180, flipVertical=true\n- step 9: patternId=square, rotation=180, flipVertical=true\n- step 10: patternId=smile, rotation=0, flipVertical=true\n- allowed patternId values for this task: star, square, N, smile, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C449"} +{"sample_id": "C450", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> E -> S -> S -> W -> N -> W -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "E", "S", "S", "W", "N", "W", "N", "E"], "observed_path_faces": [{"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C450_path_sequence.png"}, "metadata": {"level_id": 450, "name": "Reconstruct 450", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-450.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["C", "R", "Q", "8", "W", "circle"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "C", "rotation": 270}, "BOTTOM": {"patternId": "circle", "rotation": 270}, "FRONT": {"patternId": "R", "rotation": 90}, "BACK": {"patternId": "8", "rotation": 180}, "LEFT": {"patternId": "W", "rotation": 270}, "RIGHT": {"patternId": "Q", "rotation": 0}}, "bottom_faces": [{"patternId": "circle", "rotation": 270, "x": 3, "y": 1}, {"patternId": "R", "rotation": 90, "x": 3, "y": 2}, {"patternId": "W", "rotation": 270, "x": 2, "y": 2}, {"patternId": "R", "rotation": 90, "x": 3, "y": 2}, {"patternId": "C", "rotation": 270, "x": 3, "y": 3}, {"patternId": "8", "rotation": 0, "x": 3, "y": 4}, {"patternId": "W", "rotation": 90, "x": 2, "y": 4}, {"patternId": "C", "rotation": 0, "x": 2, "y": 3}, {"patternId": "R", "rotation": 180, "x": 1, "y": 3}, {"patternId": "Q", "rotation": 90, "x": 1, "y": 2}, {"patternId": "C", "rotation": 90, "x": 2, "y": 2}], "slot_sequence": ["FRONT", "LEFT", "FRONT", "TOP", "BACK", "LEFT", "TOP", "FRONT", "RIGHT", "TOP"], "required_slots": ["FRONT", "LEFT", "TOP", "BACK", "RIGHT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "C", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "R", "rotation": 90}, "BACK": {"patternId": "8", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 0}, "RIGHT": {"patternId": "Q", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "C", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "R", "rotation": 90}, "BACK": {"patternId": "8", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 0}, "RIGHT": {"patternId": "Q", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C450\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> E -> S -> S -> W -> N -> W -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=R, rotation=90, flipVertical=true\n- step 2: patternId=W, rotation=270, flipVertical=true\n- step 3: patternId=R, rotation=90, flipVertical=true\n- step 4: patternId=C, rotation=270, flipVertical=true\n- step 5: patternId=8, rotation=0, flipVertical=true\n- step 6: patternId=W, rotation=90, flipVertical=true\n- step 7: patternId=C, rotation=0, flipVertical=true\n- step 8: patternId=R, rotation=180, flipVertical=true\n- step 9: patternId=Q, rotation=90, flipVertical=true\n- step 10: patternId=C, rotation=90, flipVertical=true\n- allowed patternId values for this task: R, W, C, 8, Q, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C450"} +{"sample_id": "C451", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> N -> S -> W -> E -> N -> N -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "N", "S", "W", "E", "N", "N", "E", "N"], "observed_path_faces": [{"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C451_path_sequence.png"}, "metadata": {"level_id": 451, "name": "Reconstruct 451", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-451.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["I", "F", "U", "M", "circle", "arrow_down"], "start_x": 4, "start_y": 4, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "I", "rotation": 270}, "BOTTOM": {"patternId": "arrow_down", "rotation": 0}, "FRONT": {"patternId": "F", "rotation": 270}, "BACK": {"patternId": "M", "rotation": 270}, "LEFT": {"patternId": "circle", "rotation": 180}, "RIGHT": {"patternId": "U", "rotation": 0}}, "bottom_faces": [{"patternId": "arrow_down", "rotation": 0, "x": 4, "y": 4}, {"patternId": "circle", "rotation": 90, "x": 3, "y": 4}, {"patternId": "I", "rotation": 90, "x": 2, "y": 4}, {"patternId": "M", "rotation": 270, "x": 2, "y": 3}, {"patternId": "I", "rotation": 90, "x": 2, "y": 4}, {"patternId": "U", "rotation": 90, "x": 1, "y": 4}, {"patternId": "I", "rotation": 90, "x": 2, "y": 4}, {"patternId": "M", "rotation": 270, "x": 2, "y": 3}, {"patternId": "arrow_down", "rotation": 180, "x": 2, "y": 2}, {"patternId": "circle", "rotation": 270, "x": 3, "y": 2}, {"patternId": "F", "rotation": 0, "x": 3, "y": 1}], "slot_sequence": ["LEFT", "TOP", "BACK", "TOP", "RIGHT", "TOP", "BACK", "BOTTOM", "LEFT", "FRONT"], "required_slots": ["LEFT", "TOP", "BACK", "RIGHT", "BOTTOM", "FRONT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "I", "rotation": 270}, "BOTTOM": {"patternId": "arrow_down", "rotation": 0}, "FRONT": {"patternId": "F", "rotation": 270}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "circle", "rotation": 270}, "RIGHT": {"patternId": "U", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 270}, "BOTTOM": {"patternId": "arrow_down", "rotation": 0}, "FRONT": {"patternId": "F", "rotation": 270}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "circle", "rotation": 270}, "RIGHT": {"patternId": "U", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C451\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> N -> S -> W -> E -> N -> N -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=circle, rotation=90, flipVertical=true\n- step 2: patternId=I, rotation=90, flipVertical=true\n- step 3: patternId=M, rotation=270, flipVertical=true\n- step 4: patternId=I, rotation=90, flipVertical=true\n- step 5: patternId=U, rotation=90, flipVertical=true\n- step 6: patternId=I, rotation=90, flipVertical=true\n- step 7: patternId=M, rotation=270, flipVertical=true\n- step 8: patternId=arrow_down, rotation=180, flipVertical=true\n- step 9: patternId=circle, rotation=270, flipVertical=true\n- step 10: patternId=F, rotation=0, flipVertical=true\n- allowed patternId values for this task: circle, I, M, U, arrow_down, F, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C451"} +{"sample_id": "C452", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> S -> S -> E -> N -> N -> S -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "S", "S", "E", "N", "N", "S", "W", "W"], "observed_path_faces": [{"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C452_path_sequence.png"}, "metadata": {"level_id": 452, "name": "Reconstruct 452", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-452.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["X", "W", "L", "4", "R", "B"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "X", "rotation": 0}, "BOTTOM": {"patternId": "B", "rotation": 180}, "FRONT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "4", "rotation": 180}, "LEFT": {"patternId": "R", "rotation": 90}, "RIGHT": {"patternId": "L", "rotation": 270}}, "bottom_faces": [{"patternId": "B", "rotation": 180, "x": 3, "y": 1}, {"patternId": "W", "rotation": 90, "x": 3, "y": 2}, {"patternId": "R", "rotation": 90, "x": 2, "y": 2}, {"patternId": "X", "rotation": 270, "x": 2, "y": 3}, {"patternId": "L", "rotation": 90, "x": 2, "y": 4}, {"patternId": "W", "rotation": 270, "x": 3, "y": 4}, {"patternId": "X", "rotation": 180, "x": 3, "y": 3}, {"patternId": "4", "rotation": 180, "x": 3, "y": 2}, {"patternId": "X", "rotation": 180, "x": 3, "y": 3}, {"patternId": "L", "rotation": 0, "x": 2, "y": 3}, {"patternId": "B", "rotation": 180, "x": 1, "y": 3}], "slot_sequence": ["FRONT", "LEFT", "TOP", "RIGHT", "FRONT", "TOP", "BACK", "TOP", "RIGHT", "BOTTOM"], "required_slots": ["FRONT", "LEFT", "TOP", "RIGHT", "BACK", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "X", "rotation": 0}, "BOTTOM": {"patternId": "B", "rotation": 180}, "FRONT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "4", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 180}, "RIGHT": {"patternId": "L", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "X", "rotation": 0}, "BOTTOM": {"patternId": "B", "rotation": 180}, "FRONT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "4", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 180}, "RIGHT": {"patternId": "L", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C452\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> S -> S -> E -> N -> N -> S -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=W, rotation=90, flipVertical=true\n- step 2: patternId=R, rotation=90, flipVertical=true\n- step 3: patternId=X, rotation=270, flipVertical=true\n- step 4: patternId=L, rotation=90, flipVertical=true\n- step 5: patternId=W, rotation=270, flipVertical=true\n- step 6: patternId=X, rotation=180, flipVertical=true\n- step 7: patternId=4, rotation=180, flipVertical=true\n- step 8: patternId=X, rotation=180, flipVertical=true\n- step 9: patternId=L, rotation=0, flipVertical=true\n- step 10: patternId=B, rotation=180, flipVertical=true\n- allowed patternId values for this task: W, R, X, L, 4, B, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C452"} +{"sample_id": "C453", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> N -> E -> W -> N -> E -> E -> S -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "N", "E", "W", "N", "E", "E", "S", "S", "S"], "observed_path_faces": [{"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C453_path_sequence.png"}, "metadata": {"level_id": 453, "name": "Reconstruct 453", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-453.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["plus", "A", "O", "4", "8", "9"], "start_x": 1, "start_y": 2, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "plus", "rotation": 90}, "BOTTOM": {"patternId": "9", "rotation": 270}, "FRONT": {"patternId": "A", "rotation": 270}, "BACK": {"patternId": "4", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 90}, "RIGHT": {"patternId": "O", "rotation": 0}}, "bottom_faces": [{"patternId": "9", "rotation": 270, "x": 1, "y": 2}, {"patternId": "A", "rotation": 270, "x": 1, "y": 3}, {"patternId": "9", "rotation": 270, "x": 1, "y": 2}, {"patternId": "O", "rotation": 90, "x": 2, "y": 2}, {"patternId": "9", "rotation": 270, "x": 1, "y": 2}, {"patternId": "4", "rotation": 180, "x": 1, "y": 1}, {"patternId": "O", "rotation": 180, "x": 2, "y": 1}, {"patternId": "A", "rotation": 90, "x": 3, "y": 1}, {"patternId": "9", "rotation": 90, "x": 3, "y": 2}, {"patternId": "4", "rotation": 0, "x": 3, "y": 3}, {"patternId": "plus", "rotation": 270, "x": 3, "y": 4}], "slot_sequence": ["FRONT", "BOTTOM", "RIGHT", "BOTTOM", "BACK", "RIGHT", "FRONT", "BOTTOM", "BACK", "TOP"], "required_slots": ["FRONT", "BOTTOM", "RIGHT", "BACK", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "plus", "rotation": 90}, "BOTTOM": {"patternId": "9", "rotation": 270}, "FRONT": {"patternId": "A", "rotation": 270}, "BACK": {"patternId": "4", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "plus", "rotation": 90}, "BOTTOM": {"patternId": "9", "rotation": 270}, "FRONT": {"patternId": "A", "rotation": 270}, "BACK": {"patternId": "4", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C453\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> N -> E -> W -> N -> E -> E -> S -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=A, rotation=270, flipVertical=true\n- step 2: patternId=9, rotation=270, flipVertical=true\n- step 3: patternId=O, rotation=90, flipVertical=true\n- step 4: patternId=9, rotation=270, flipVertical=true\n- step 5: patternId=4, rotation=180, flipVertical=true\n- step 6: patternId=O, rotation=180, flipVertical=true\n- step 7: patternId=A, rotation=90, flipVertical=true\n- step 8: patternId=9, rotation=90, flipVertical=true\n- step 9: patternId=4, rotation=0, flipVertical=true\n- step 10: patternId=plus, rotation=270, flipVertical=true\n- allowed patternId values for this task: A, 9, O, 4, plus, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C453"} +{"sample_id": "C454", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> E -> S -> E -> W -> S -> E -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "E", "S", "E", "W", "S", "E", "S", "W"], "observed_path_faces": [{"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C454_path_sequence.png"}, "metadata": {"level_id": 454, "name": "Reconstruct 454", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-454.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["N", "J", "arrow_left", "R", "W", "arrow_left"], "start_x": 1, "start_y": 3, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "N", "rotation": 270}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 90}, "LEFT": {"patternId": "W", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 180}}, "bottom_faces": [{"patternId": "arrow_left", "rotation": 0, "x": 1, "y": 3}, {"patternId": "R", "rotation": 270, "x": 1, "y": 2}, {"patternId": "N", "rotation": 270, "x": 1, "y": 1}, {"patternId": "arrow_left", "rotation": 90, "x": 2, "y": 1}, {"patternId": "R", "rotation": 0, "x": 2, "y": 2}, {"patternId": "arrow_left", "rotation": 90, "x": 3, "y": 2}, {"patternId": "R", "rotation": 0, "x": 2, "y": 2}, {"patternId": "W", "rotation": 270, "x": 2, "y": 3}, {"patternId": "arrow_left", "rotation": 0, "x": 3, "y": 3}, {"patternId": "J", "rotation": 0, "x": 3, "y": 4}, {"patternId": "W", "rotation": 0, "x": 2, "y": 4}], "slot_sequence": ["BACK", "TOP", "RIGHT", "BACK", "BOTTOM", "BACK", "LEFT", "BOTTOM", "FRONT", "LEFT"], "required_slots": ["BACK", "TOP", "RIGHT", "BOTTOM", "LEFT", "FRONT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "N", "rotation": 270}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 270}, "LEFT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "arrow_left", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "N", "rotation": 270}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 270}, "LEFT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "arrow_left", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C454\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> E -> S -> E -> W -> S -> E -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=R, rotation=270, flipVertical=true\n- step 2: patternId=N, rotation=270, flipVertical=true\n- step 3: patternId=arrow_left, rotation=90, flipVertical=true\n- step 4: patternId=R, rotation=0, flipVertical=true\n- step 5: patternId=arrow_left, rotation=90, flipVertical=true\n- step 6: patternId=R, rotation=0, flipVertical=true\n- step 7: patternId=W, rotation=270, flipVertical=true\n- step 8: patternId=arrow_left, rotation=0, flipVertical=true\n- step 9: patternId=J, rotation=0, flipVertical=true\n- step 10: patternId=W, rotation=0, flipVertical=true\n- allowed patternId values for this task: R, N, arrow_left, W, J, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C454"} +{"sample_id": "C455", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> N -> N -> W -> S -> N -> W -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "N", "N", "W", "S", "N", "W", "S", "S"], "observed_path_faces": [{"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C455_path_sequence.png"}, "metadata": {"level_id": 455, "name": "Reconstruct 455", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-455.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["S", "star", "G", "diamond", "J", "star"], "start_x": 2, "start_y": 2, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "S", "rotation": 0}, "BOTTOM": {"patternId": "star", "rotation": 90}, "FRONT": {"patternId": "star", "rotation": 180}, "BACK": {"patternId": "diamond", "rotation": 0}, "LEFT": {"patternId": "J", "rotation": 0}, "RIGHT": {"patternId": "G", "rotation": 90}}, "bottom_faces": [{"patternId": "star", "rotation": 90, "x": 2, "y": 2}, {"patternId": "G", "rotation": 180, "x": 3, "y": 2}, {"patternId": "star", "rotation": 270, "x": 3, "y": 3}, {"patternId": "G", "rotation": 180, "x": 3, "y": 2}, {"patternId": "diamond", "rotation": 90, "x": 3, "y": 1}, {"patternId": "star", "rotation": 0, "x": 2, "y": 1}, {"patternId": "G", "rotation": 90, "x": 2, "y": 2}, {"patternId": "star", "rotation": 0, "x": 2, "y": 1}, {"patternId": "star", "rotation": 90, "x": 1, "y": 1}, {"patternId": "G", "rotation": 0, "x": 1, "y": 2}, {"patternId": "diamond", "rotation": 270, "x": 1, "y": 3}], "slot_sequence": ["RIGHT", "FRONT", "RIGHT", "BACK", "BOTTOM", "RIGHT", "BOTTOM", "FRONT", "RIGHT", "BACK"], "required_slots": ["RIGHT", "FRONT", "BACK", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "star", "rotation": 90}, "FRONT": {"patternId": "star", "rotation": 180}, "BACK": {"patternId": "diamond", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "G", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "star", "rotation": 90}, "FRONT": {"patternId": "star", "rotation": 180}, "BACK": {"patternId": "diamond", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "G", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C455\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> N -> N -> W -> S -> N -> W -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=G, rotation=180, flipVertical=true\n- step 2: patternId=star, rotation=270, flipVertical=true\n- step 3: patternId=G, rotation=180, flipVertical=true\n- step 4: patternId=diamond, rotation=90, flipVertical=true\n- step 5: patternId=star, rotation=0, flipVertical=true\n- step 6: patternId=G, rotation=90, flipVertical=true\n- step 7: patternId=star, rotation=0, flipVertical=true\n- step 8: patternId=star, rotation=90, flipVertical=true\n- step 9: patternId=G, rotation=0, flipVertical=true\n- step 10: patternId=diamond, rotation=270, flipVertical=true\n- allowed patternId values for this task: G, star, diamond, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C455"} +{"sample_id": "C456", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> E -> E -> N -> E -> W -> N -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "E", "E", "N", "E", "W", "N", "E", "E"], "observed_path_faces": [{"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C456_path_sequence.png"}, "metadata": {"level_id": 456, "name": "Reconstruct 456", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-456.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["J", "B", "9", "star", "Z", "smile"], "start_x": 2, "start_y": 2, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "J", "rotation": 270}, "BOTTOM": {"patternId": "smile", "rotation": 90}, "FRONT": {"patternId": "B", "rotation": 270}, "BACK": {"patternId": "star", "rotation": 270}, "LEFT": {"patternId": "Z", "rotation": 270}, "RIGHT": {"patternId": "9", "rotation": 0}}, "bottom_faces": [{"patternId": "smile", "rotation": 90, "x": 2, "y": 2}, {"patternId": "B", "rotation": 270, "x": 2, "y": 3}, {"patternId": "Z", "rotation": 270, "x": 1, "y": 3}, {"patternId": "B", "rotation": 270, "x": 2, "y": 3}, {"patternId": "9", "rotation": 0, "x": 3, "y": 3}, {"patternId": "smile", "rotation": 0, "x": 3, "y": 2}, {"patternId": "star", "rotation": 0, "x": 4, "y": 2}, {"patternId": "smile", "rotation": 0, "x": 3, "y": 2}, {"patternId": "Z", "rotation": 90, "x": 3, "y": 1}, {"patternId": "star", "rotation": 90, "x": 4, "y": 1}, {"patternId": "9", "rotation": 180, "x": 5, "y": 1}], "slot_sequence": ["FRONT", "LEFT", "FRONT", "RIGHT", "BOTTOM", "BACK", "BOTTOM", "LEFT", "BACK", "RIGHT"], "required_slots": ["FRONT", "LEFT", "RIGHT", "BOTTOM", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "smile", "rotation": 90}, "FRONT": {"patternId": "B", "rotation": 270}, "BACK": {"patternId": "star", "rotation": 90}, "LEFT": {"patternId": "Z", "rotation": 0}, "RIGHT": {"patternId": "9", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "smile", "rotation": 90}, "FRONT": {"patternId": "B", "rotation": 270}, "BACK": {"patternId": "star", "rotation": 90}, "LEFT": {"patternId": "Z", "rotation": 0}, "RIGHT": {"patternId": "9", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C456\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> E -> E -> N -> E -> W -> N -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=B, rotation=270, flipVertical=true\n- step 2: patternId=Z, rotation=270, flipVertical=true\n- step 3: patternId=B, rotation=270, flipVertical=true\n- step 4: patternId=9, rotation=0, flipVertical=true\n- step 5: patternId=smile, rotation=0, flipVertical=true\n- step 6: patternId=star, rotation=0, flipVertical=true\n- step 7: patternId=smile, rotation=0, flipVertical=true\n- step 8: patternId=Z, rotation=90, flipVertical=true\n- step 9: patternId=star, rotation=90, flipVertical=true\n- step 10: patternId=9, rotation=180, flipVertical=true\n- allowed patternId values for this task: B, Z, 9, smile, star, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C456"} +{"sample_id": "C457", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> S -> W -> S -> S -> S -> E -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "S", "W", "S", "S", "S", "E", "S", "W"], "observed_path_faces": [{"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C457_path_sequence.png"}, "metadata": {"level_id": 457, "name": "Reconstruct 457", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-457.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["X", "arrow_up", "smile", "7", "3", "K"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 9, "true_solution_faces": {"TOP": {"patternId": "X", "rotation": 0}, "BOTTOM": {"patternId": "K", "rotation": 270}, "FRONT": {"patternId": "arrow_up", "rotation": 270}, "BACK": {"patternId": "7", "rotation": 90}, "LEFT": {"patternId": "3", "rotation": 90}, "RIGHT": {"patternId": "smile", "rotation": 90}}, "bottom_faces": [{"patternId": "K", "rotation": 270, "x": 3, "y": 1}, {"patternId": "3", "rotation": 0, "x": 2, "y": 1}, {"patternId": "arrow_up", "rotation": 180, "x": 2, "y": 2}, {"patternId": "smile", "rotation": 0, "x": 2, "y": 3}, {"patternId": "X", "rotation": 0, "x": 1, "y": 3}, {"patternId": "7", "rotation": 270, "x": 1, "y": 4}, {"patternId": "K", "rotation": 270, "x": 1, "y": 5}, {"patternId": "arrow_up", "rotation": 270, "x": 1, "y": 6}, {"patternId": "smile", "rotation": 90, "x": 2, "y": 6}, {"patternId": "X", "rotation": 90, "x": 2, "y": 7}, {"patternId": "arrow_up", "rotation": 0, "x": 1, "y": 7}], "slot_sequence": ["LEFT", "FRONT", "RIGHT", "TOP", "BACK", "BOTTOM", "FRONT", "RIGHT", "TOP", "FRONT"], "required_slots": ["LEFT", "FRONT", "RIGHT", "TOP", "BACK", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "X", "rotation": 0}, "BOTTOM": {"patternId": "K", "rotation": 270}, "FRONT": {"patternId": "arrow_up", "rotation": 270}, "BACK": {"patternId": "7", "rotation": 270}, "LEFT": {"patternId": "3", "rotation": 180}, "RIGHT": {"patternId": "smile", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "X", "rotation": 0}, "BOTTOM": {"patternId": "K", "rotation": 270}, "FRONT": {"patternId": "arrow_up", "rotation": 270}, "BACK": {"patternId": "7", "rotation": 270}, "LEFT": {"patternId": "3", "rotation": 180}, "RIGHT": {"patternId": "smile", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C457\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> S -> W -> S -> S -> S -> E -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=3, rotation=0, flipVertical=true\n- step 2: patternId=arrow_up, rotation=180, flipVertical=true\n- step 3: patternId=smile, rotation=0, flipVertical=true\n- step 4: patternId=X, rotation=0, flipVertical=true\n- step 5: patternId=7, rotation=270, flipVertical=true\n- step 6: patternId=K, rotation=270, flipVertical=true\n- step 7: patternId=arrow_up, rotation=270, flipVertical=true\n- step 8: patternId=smile, rotation=90, flipVertical=true\n- step 9: patternId=X, rotation=90, flipVertical=true\n- step 10: patternId=arrow_up, rotation=0, flipVertical=true\n- allowed patternId values for this task: 3, arrow_up, smile, X, 7, K, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C457"} +{"sample_id": "C458", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> N -> W -> S -> S -> W -> W -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "N", "W", "S", "S", "W", "W", "N", "W"], "observed_path_faces": [{"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C458_path_sequence.png"}, "metadata": {"level_id": 458, "name": "Reconstruct 458", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-458.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["smile", "F", "P", "heart", "5", "J"], "start_x": 4, "start_y": 3, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "smile", "rotation": 270}, "BOTTOM": {"patternId": "J", "rotation": 90}, "FRONT": {"patternId": "F", "rotation": 180}, "BACK": {"patternId": "heart", "rotation": 90}, "LEFT": {"patternId": "5", "rotation": 270}, "RIGHT": {"patternId": "P", "rotation": 270}}, "bottom_faces": [{"patternId": "J", "rotation": 90, "x": 4, "y": 3}, {"patternId": "heart", "rotation": 270, "x": 4, "y": 2}, {"patternId": "P", "rotation": 90, "x": 5, "y": 2}, {"patternId": "smile", "rotation": 180, "x": 5, "y": 1}, {"patternId": "heart", "rotation": 180, "x": 4, "y": 1}, {"patternId": "P", "rotation": 0, "x": 4, "y": 2}, {"patternId": "F", "rotation": 270, "x": 4, "y": 3}, {"patternId": "J", "rotation": 180, "x": 3, "y": 3}, {"patternId": "heart", "rotation": 0, "x": 2, "y": 3}, {"patternId": "P", "rotation": 180, "x": 2, "y": 2}, {"patternId": "smile", "rotation": 270, "x": 1, "y": 2}], "slot_sequence": ["BACK", "RIGHT", "TOP", "BACK", "RIGHT", "FRONT", "BOTTOM", "BACK", "RIGHT", "TOP"], "required_slots": ["BACK", "RIGHT", "TOP", "FRONT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "smile", "rotation": 270}, "BOTTOM": {"patternId": "J", "rotation": 90}, "FRONT": {"patternId": "F", "rotation": 180}, "BACK": {"patternId": "heart", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "P", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 270}, "BOTTOM": {"patternId": "J", "rotation": 90}, "FRONT": {"patternId": "F", "rotation": 180}, "BACK": {"patternId": "heart", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "P", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C458\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> N -> W -> S -> S -> W -> W -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=heart, rotation=270, flipVertical=true\n- step 2: patternId=P, rotation=90, flipVertical=true\n- step 3: patternId=smile, rotation=180, flipVertical=true\n- step 4: patternId=heart, rotation=180, flipVertical=true\n- step 5: patternId=P, rotation=0, flipVertical=true\n- step 6: patternId=F, rotation=270, flipVertical=true\n- step 7: patternId=J, rotation=180, flipVertical=true\n- step 8: patternId=heart, rotation=0, flipVertical=true\n- step 9: patternId=P, rotation=180, flipVertical=true\n- step 10: patternId=smile, rotation=270, flipVertical=true\n- allowed patternId values for this task: heart, P, smile, F, J, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C458"} +{"sample_id": "C459", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> S -> N -> S -> E -> E -> E -> S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "S", "N", "S", "E", "E", "E", "S", "N"], "observed_path_faces": [{"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C459_path_sequence.png"}, "metadata": {"level_id": 459, "name": "Reconstruct 459", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-459.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["smile", "Z", "S", "star", "L", "X"], "start_x": 1, "start_y": 2, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "smile", "rotation": 0}, "BOTTOM": {"patternId": "X", "rotation": 90}, "FRONT": {"patternId": "Z", "rotation": 270}, "BACK": {"patternId": "star", "rotation": 0}, "LEFT": {"patternId": "L", "rotation": 180}, "RIGHT": {"patternId": "S", "rotation": 180}}, "bottom_faces": [{"patternId": "X", "rotation": 90, "x": 1, "y": 2}, {"patternId": "star", "rotation": 180, "x": 1, "y": 1}, {"patternId": "S", "rotation": 0, "x": 2, "y": 1}, {"patternId": "X", "rotation": 180, "x": 2, "y": 2}, {"patternId": "S", "rotation": 0, "x": 2, "y": 1}, {"patternId": "X", "rotation": 180, "x": 2, "y": 2}, {"patternId": "Z", "rotation": 0, "x": 3, "y": 2}, {"patternId": "smile", "rotation": 90, "x": 4, "y": 2}, {"patternId": "star", "rotation": 270, "x": 5, "y": 2}, {"patternId": "L", "rotation": 90, "x": 5, "y": 3}, {"patternId": "star", "rotation": 270, "x": 5, "y": 2}], "slot_sequence": ["BACK", "RIGHT", "BOTTOM", "RIGHT", "BOTTOM", "FRONT", "TOP", "BACK", "LEFT", "BACK"], "required_slots": ["BACK", "RIGHT", "BOTTOM", "FRONT", "TOP", "LEFT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "smile", "rotation": 0}, "BOTTOM": {"patternId": "X", "rotation": 90}, "FRONT": {"patternId": "Z", "rotation": 270}, "BACK": {"patternId": "star", "rotation": 180}, "LEFT": {"patternId": "L", "rotation": 270}, "RIGHT": {"patternId": "S", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 0}, "BOTTOM": {"patternId": "X", "rotation": 90}, "FRONT": {"patternId": "Z", "rotation": 270}, "BACK": {"patternId": "star", "rotation": 180}, "LEFT": {"patternId": "L", "rotation": 270}, "RIGHT": {"patternId": "S", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C459\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> S -> N -> S -> E -> E -> E -> S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=star, rotation=180, flipVertical=true\n- step 2: patternId=S, rotation=0, flipVertical=true\n- step 3: patternId=X, rotation=180, flipVertical=true\n- step 4: patternId=S, rotation=0, flipVertical=true\n- step 5: patternId=X, rotation=180, flipVertical=true\n- step 6: patternId=Z, rotation=0, flipVertical=true\n- step 7: patternId=smile, rotation=90, flipVertical=true\n- step 8: patternId=star, rotation=270, flipVertical=true\n- step 9: patternId=L, rotation=90, flipVertical=true\n- step 10: patternId=star, rotation=270, flipVertical=true\n- allowed patternId values for this task: star, S, X, Z, smile, L, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C459"} +{"sample_id": "C460", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> N -> S -> E -> S -> E -> S -> S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "N", "S", "E", "S", "E", "S", "S", "N"], "observed_path_faces": [{"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C460_path_sequence.png"}, "metadata": {"level_id": 460, "name": "Reconstruct 460", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-460.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["7", "H", "B", "1", "P", "D"], "start_x": 1, "start_y": 4, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "7", "rotation": 0}, "BOTTOM": {"patternId": "D", "rotation": 180}, "FRONT": {"patternId": "H", "rotation": 0}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "P", "rotation": 270}, "RIGHT": {"patternId": "B", "rotation": 0}}, "bottom_faces": [{"patternId": "D", "rotation": 180, "x": 1, "y": 4}, {"patternId": "1", "rotation": 0, "x": 1, "y": 3}, {"patternId": "7", "rotation": 0, "x": 1, "y": 2}, {"patternId": "H", "rotation": 0, "x": 1, "y": 1}, {"patternId": "7", "rotation": 0, "x": 1, "y": 2}, {"patternId": "B", "rotation": 270, "x": 2, "y": 2}, {"patternId": "1", "rotation": 90, "x": 2, "y": 3}, {"patternId": "D", "rotation": 270, "x": 3, "y": 3}, {"patternId": "P", "rotation": 270, "x": 3, "y": 4}, {"patternId": "7", "rotation": 270, "x": 3, "y": 5}, {"patternId": "P", "rotation": 270, "x": 3, "y": 4}], "slot_sequence": ["BACK", "TOP", "FRONT", "TOP", "RIGHT", "BACK", "BOTTOM", "LEFT", "TOP", "LEFT"], "required_slots": ["BACK", "TOP", "FRONT", "RIGHT", "BOTTOM", "LEFT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "7", "rotation": 0}, "BOTTOM": {"patternId": "D", "rotation": 180}, "FRONT": {"patternId": "H", "rotation": 0}, "BACK": {"patternId": "1", "rotation": 0}, "LEFT": {"patternId": "P", "rotation": 0}, "RIGHT": {"patternId": "B", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "7", "rotation": 0}, "BOTTOM": {"patternId": "D", "rotation": 180}, "FRONT": {"patternId": "H", "rotation": 0}, "BACK": {"patternId": "1", "rotation": 0}, "LEFT": {"patternId": "P", "rotation": 0}, "RIGHT": {"patternId": "B", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C460\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> N -> S -> E -> S -> E -> S -> S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=1, rotation=0, flipVertical=true\n- step 2: patternId=7, rotation=0, flipVertical=true\n- step 3: patternId=H, rotation=0, flipVertical=true\n- step 4: patternId=7, rotation=0, flipVertical=true\n- step 5: patternId=B, rotation=270, flipVertical=true\n- step 6: patternId=1, rotation=90, flipVertical=true\n- step 7: patternId=D, rotation=270, flipVertical=true\n- step 8: patternId=P, rotation=270, flipVertical=true\n- step 9: patternId=7, rotation=270, flipVertical=true\n- step 10: patternId=P, rotation=270, flipVertical=true\n- allowed patternId values for this task: 1, 7, H, B, D, P, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C460"} +{"sample_id": "C461", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> N -> E -> N -> N -> E -> E -> N -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "N", "E", "N", "N", "E", "E", "N", "S"], "observed_path_faces": [{"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C461_path_sequence.png"}, "metadata": {"level_id": 461, "name": "Reconstruct 461", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-461.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["plus", "K", "A", "diamond", "diamond", "triangle"], "start_x": 1, "start_y": 5, "grid_width": 8, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "plus", "rotation": 90}, "BOTTOM": {"patternId": "triangle", "rotation": 0}, "FRONT": {"patternId": "K", "rotation": 90}, "BACK": {"patternId": "diamond", "rotation": 0}, "LEFT": {"patternId": "diamond", "rotation": 180}, "RIGHT": {"patternId": "A", "rotation": 0}}, "bottom_faces": [{"patternId": "triangle", "rotation": 0, "x": 1, "y": 5}, {"patternId": "A", "rotation": 90, "x": 2, "y": 5}, {"patternId": "plus", "rotation": 270, "x": 3, "y": 5}, {"patternId": "diamond", "rotation": 0, "x": 3, "y": 4}, {"patternId": "diamond", "rotation": 180, "x": 4, "y": 4}, {"patternId": "triangle", "rotation": 90, "x": 4, "y": 3}, {"patternId": "A", "rotation": 180, "x": 4, "y": 2}, {"patternId": "K", "rotation": 270, "x": 5, "y": 2}, {"patternId": "diamond", "rotation": 0, "x": 6, "y": 2}, {"patternId": "plus", "rotation": 180, "x": 6, "y": 1}, {"patternId": "diamond", "rotation": 0, "x": 6, "y": 2}], "slot_sequence": ["RIGHT", "TOP", "BACK", "LEFT", "BOTTOM", "RIGHT", "FRONT", "LEFT", "TOP", "LEFT"], "required_slots": ["RIGHT", "TOP", "BACK", "LEFT", "BOTTOM", "FRONT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "plus", "rotation": 90}, "BOTTOM": {"patternId": "triangle", "rotation": 0}, "FRONT": {"patternId": "K", "rotation": 90}, "BACK": {"patternId": "diamond", "rotation": 180}, "LEFT": {"patternId": "diamond", "rotation": 270}, "RIGHT": {"patternId": "A", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "plus", "rotation": 90}, "BOTTOM": {"patternId": "triangle", "rotation": 0}, "FRONT": {"patternId": "K", "rotation": 90}, "BACK": {"patternId": "diamond", "rotation": 180}, "LEFT": {"patternId": "diamond", "rotation": 270}, "RIGHT": {"patternId": "A", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C461\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> N -> E -> N -> N -> E -> E -> N -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=A, rotation=90, flipVertical=true\n- step 2: patternId=plus, rotation=270, flipVertical=true\n- step 3: patternId=diamond, rotation=0, flipVertical=true\n- step 4: patternId=diamond, rotation=180, flipVertical=true\n- step 5: patternId=triangle, rotation=90, flipVertical=true\n- step 6: patternId=A, rotation=180, flipVertical=true\n- step 7: patternId=K, rotation=270, flipVertical=true\n- step 8: patternId=diamond, rotation=0, flipVertical=true\n- step 9: patternId=plus, rotation=180, flipVertical=true\n- step 10: patternId=diamond, rotation=0, flipVertical=true\n- allowed patternId values for this task: A, plus, diamond, triangle, K, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C461"} +{"sample_id": "C462", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> N -> S -> W -> S -> E -> S -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "N", "S", "W", "S", "E", "S", "W", "N"], "observed_path_faces": [{"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C462_path_sequence.png"}, "metadata": {"level_id": 462, "name": "Reconstruct 462", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-462.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["E", "1", "arrow_right", "P", "8", "5"], "start_x": 3, "start_y": 1, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "E", "rotation": 0}, "BOTTOM": {"patternId": "5", "rotation": 270}, "FRONT": {"patternId": "1", "rotation": 90}, "BACK": {"patternId": "P", "rotation": 90}, "LEFT": {"patternId": "8", "rotation": 180}, "RIGHT": {"patternId": "arrow_right", "rotation": 0}}, "bottom_faces": [{"patternId": "5", "rotation": 270, "x": 3, "y": 1}, {"patternId": "8", "rotation": 90, "x": 2, "y": 1}, {"patternId": "1", "rotation": 0, "x": 2, "y": 2}, {"patternId": "8", "rotation": 90, "x": 2, "y": 1}, {"patternId": "1", "rotation": 0, "x": 2, "y": 2}, {"patternId": "E", "rotation": 270, "x": 1, "y": 2}, {"patternId": "arrow_right", "rotation": 180, "x": 1, "y": 3}, {"patternId": "1", "rotation": 270, "x": 2, "y": 3}, {"patternId": "5", "rotation": 90, "x": 2, "y": 4}, {"patternId": "arrow_right", "rotation": 270, "x": 1, "y": 4}, {"patternId": "1", "rotation": 0, "x": 1, "y": 3}], "slot_sequence": ["LEFT", "FRONT", "LEFT", "FRONT", "TOP", "RIGHT", "FRONT", "BOTTOM", "RIGHT", "FRONT"], "required_slots": ["LEFT", "FRONT", "TOP", "RIGHT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "E", "rotation": 0}, "BOTTOM": {"patternId": "5", "rotation": 270}, "FRONT": {"patternId": "1", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 270}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "E", "rotation": 0}, "BOTTOM": {"patternId": "5", "rotation": 270}, "FRONT": {"patternId": "1", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 270}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C462\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> N -> S -> W -> S -> E -> S -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=8, rotation=90, flipVertical=true\n- step 2: patternId=1, rotation=0, flipVertical=true\n- step 3: patternId=8, rotation=90, flipVertical=true\n- step 4: patternId=1, rotation=0, flipVertical=true\n- step 5: patternId=E, rotation=270, flipVertical=true\n- step 6: patternId=arrow_right, rotation=180, flipVertical=true\n- step 7: patternId=1, rotation=270, flipVertical=true\n- step 8: patternId=5, rotation=90, flipVertical=true\n- step 9: patternId=arrow_right, rotation=270, flipVertical=true\n- step 10: patternId=1, rotation=0, flipVertical=true\n- allowed patternId values for this task: 8, 1, E, arrow_right, 5, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C462"} +{"sample_id": "C463", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> N -> W -> S -> S -> E -> S -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "N", "W", "S", "S", "E", "S", "E", "S"], "observed_path_faces": [{"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C463_path_sequence.png"}, "metadata": {"level_id": 463, "name": "Reconstruct 463", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-463.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["D", "I", "D", "T", "circle", "J"], "start_x": 2, "start_y": 1, "grid_width": 5, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "D", "rotation": 0}, "BOTTOM": {"patternId": "J", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 270}, "BACK": {"patternId": "T", "rotation": 270}, "LEFT": {"patternId": "circle", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 270}}, "bottom_faces": [{"patternId": "J", "rotation": 0, "x": 2, "y": 1}, {"patternId": "I", "rotation": 270, "x": 2, "y": 2}, {"patternId": "D", "rotation": 0, "x": 2, "y": 3}, {"patternId": "I", "rotation": 270, "x": 2, "y": 2}, {"patternId": "circle", "rotation": 0, "x": 1, "y": 2}, {"patternId": "D", "rotation": 270, "x": 1, "y": 3}, {"patternId": "D", "rotation": 90, "x": 1, "y": 4}, {"patternId": "I", "rotation": 90, "x": 2, "y": 4}, {"patternId": "J", "rotation": 180, "x": 2, "y": 5}, {"patternId": "circle", "rotation": 90, "x": 3, "y": 5}, {"patternId": "T", "rotation": 0, "x": 3, "y": 6}], "slot_sequence": ["FRONT", "TOP", "FRONT", "LEFT", "TOP", "RIGHT", "FRONT", "BOTTOM", "LEFT", "BACK"], "required_slots": ["FRONT", "TOP", "LEFT", "RIGHT", "BOTTOM", "BACK"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "D", "rotation": 0}, "BOTTOM": {"patternId": "J", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 270}, "BACK": {"patternId": "T", "rotation": 90}, "LEFT": {"patternId": "circle", "rotation": 90}, "RIGHT": {"patternId": "D", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "D", "rotation": 0}, "BOTTOM": {"patternId": "J", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 270}, "BACK": {"patternId": "T", "rotation": 90}, "LEFT": {"patternId": "circle", "rotation": 90}, "RIGHT": {"patternId": "D", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C463\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> N -> W -> S -> S -> E -> S -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=I, rotation=270, flipVertical=true\n- step 2: patternId=D, rotation=0, flipVertical=true\n- step 3: patternId=I, rotation=270, flipVertical=true\n- step 4: patternId=circle, rotation=0, flipVertical=true\n- step 5: patternId=D, rotation=270, flipVertical=true\n- step 6: patternId=D, rotation=90, flipVertical=true\n- step 7: patternId=I, rotation=90, flipVertical=true\n- step 8: patternId=J, rotation=180, flipVertical=true\n- step 9: patternId=circle, rotation=90, flipVertical=true\n- step 10: patternId=T, rotation=0, flipVertical=true\n- allowed patternId values for this task: I, D, circle, J, T, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C463"} +{"sample_id": "C464", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> E -> N -> S -> W -> E -> W -> S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "E", "N", "S", "W", "E", "W", "S", "N"], "observed_path_faces": [{"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C464_path_sequence.png"}, "metadata": {"level_id": 464, "name": "Reconstruct 464", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-464.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["O", "square", "T", "U", "Z", "1"], "start_x": 1, "start_y": 1, "grid_width": 4, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "O", "rotation": 90}, "BOTTOM": {"patternId": "1", "rotation": 180}, "FRONT": {"patternId": "square", "rotation": 180}, "BACK": {"patternId": "U", "rotation": 0}, "LEFT": {"patternId": "Z", "rotation": 90}, "RIGHT": {"patternId": "T", "rotation": 180}}, "bottom_faces": [{"patternId": "1", "rotation": 180, "x": 1, "y": 1}, {"patternId": "square", "rotation": 180, "x": 1, "y": 2}, {"patternId": "O", "rotation": 90, "x": 1, "y": 3}, {"patternId": "T", "rotation": 90, "x": 2, "y": 3}, {"patternId": "square", "rotation": 90, "x": 2, "y": 2}, {"patternId": "T", "rotation": 90, "x": 2, "y": 3}, {"patternId": "O", "rotation": 90, "x": 1, "y": 3}, {"patternId": "T", "rotation": 90, "x": 2, "y": 3}, {"patternId": "O", "rotation": 90, "x": 1, "y": 3}, {"patternId": "U", "rotation": 180, "x": 1, "y": 4}, {"patternId": "O", "rotation": 90, "x": 1, "y": 3}], "slot_sequence": ["FRONT", "TOP", "RIGHT", "FRONT", "RIGHT", "TOP", "RIGHT", "TOP", "BACK", "TOP"], "required_slots": ["FRONT", "TOP", "RIGHT", "BACK"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "O", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 180}, "BACK": {"patternId": "U", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "T", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 180}, "BACK": {"patternId": "U", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "T", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C464\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> E -> N -> S -> W -> E -> W -> S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=square, rotation=180, flipVertical=true\n- step 2: patternId=O, rotation=90, flipVertical=true\n- step 3: patternId=T, rotation=90, flipVertical=true\n- step 4: patternId=square, rotation=90, flipVertical=true\n- step 5: patternId=T, rotation=90, flipVertical=true\n- step 6: patternId=O, rotation=90, flipVertical=true\n- step 7: patternId=T, rotation=90, flipVertical=true\n- step 8: patternId=O, rotation=90, flipVertical=true\n- step 9: patternId=U, rotation=180, flipVertical=true\n- step 10: patternId=O, rotation=90, flipVertical=true\n- allowed patternId values for this task: square, O, T, U, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C464"} +{"sample_id": "C465", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> S -> S -> E -> S -> N -> E -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "S", "S", "E", "S", "N", "E", "E", "S"], "observed_path_faces": [{"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C465_path_sequence.png"}, "metadata": {"level_id": 465, "name": "Reconstruct 465", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-465.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["U", "G", "I", "B", "M", "G"], "start_x": 2, "start_y": 2, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "U", "rotation": 270}, "BOTTOM": {"patternId": "G", "rotation": 90}, "FRONT": {"patternId": "G", "rotation": 270}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "M", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 270}}, "bottom_faces": [{"patternId": "G", "rotation": 90, "x": 2, "y": 2}, {"patternId": "B", "rotation": 180, "x": 2, "y": 1}, {"patternId": "M", "rotation": 180, "x": 1, "y": 1}, {"patternId": "G", "rotation": 0, "x": 1, "y": 2}, {"patternId": "I", "rotation": 270, "x": 1, "y": 3}, {"patternId": "B", "rotation": 0, "x": 2, "y": 3}, {"patternId": "U", "rotation": 90, "x": 2, "y": 4}, {"patternId": "B", "rotation": 0, "x": 2, "y": 3}, {"patternId": "M", "rotation": 0, "x": 3, "y": 3}, {"patternId": "G", "rotation": 270, "x": 4, "y": 3}, {"patternId": "U", "rotation": 270, "x": 4, "y": 4}], "slot_sequence": ["BACK", "LEFT", "BOTTOM", "RIGHT", "BACK", "TOP", "BACK", "LEFT", "FRONT", "TOP"], "required_slots": ["BACK", "LEFT", "BOTTOM", "RIGHT", "TOP", "FRONT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "U", "rotation": 270}, "BOTTOM": {"patternId": "G", "rotation": 90}, "FRONT": {"patternId": "G", "rotation": 270}, "BACK": {"patternId": "B", "rotation": 180}, "LEFT": {"patternId": "M", "rotation": 90}, "RIGHT": {"patternId": "I", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "U", "rotation": 270}, "BOTTOM": {"patternId": "G", "rotation": 90}, "FRONT": {"patternId": "G", "rotation": 270}, "BACK": {"patternId": "B", "rotation": 180}, "LEFT": {"patternId": "M", "rotation": 90}, "RIGHT": {"patternId": "I", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C465\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> S -> S -> E -> S -> N -> E -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=B, rotation=180, flipVertical=true\n- step 2: patternId=M, rotation=180, flipVertical=true\n- step 3: patternId=G, rotation=0, flipVertical=true\n- step 4: patternId=I, rotation=270, flipVertical=true\n- step 5: patternId=B, rotation=0, flipVertical=true\n- step 6: patternId=U, rotation=90, flipVertical=true\n- step 7: patternId=B, rotation=0, flipVertical=true\n- step 8: patternId=M, rotation=0, flipVertical=true\n- step 9: patternId=G, rotation=270, flipVertical=true\n- step 10: patternId=U, rotation=270, flipVertical=true\n- allowed patternId values for this task: B, M, G, I, U, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C465"} +{"sample_id": "C466", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> E -> N -> E -> S -> E -> E -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "E", "N", "E", "S", "E", "E", "S", "W"], "observed_path_faces": [{"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C466_path_sequence.png"}, "metadata": {"level_id": 466, "name": "Reconstruct 466", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-466.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["P", "8", "smile", "smile", "E", "E"], "start_x": 1, "start_y": 1, "grid_width": 8, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "P", "rotation": 270}, "BOTTOM": {"patternId": "E", "rotation": 270}, "FRONT": {"patternId": "8", "rotation": 0}, "BACK": {"patternId": "smile", "rotation": 270}, "LEFT": {"patternId": "E", "rotation": 180}, "RIGHT": {"patternId": "smile", "rotation": 270}}, "bottom_faces": [{"patternId": "E", "rotation": 270, "x": 1, "y": 1}, {"patternId": "8", "rotation": 0, "x": 1, "y": 2}, {"patternId": "smile", "rotation": 270, "x": 2, "y": 2}, {"patternId": "smile", "rotation": 270, "x": 3, "y": 2}, {"patternId": "E", "rotation": 90, "x": 3, "y": 1}, {"patternId": "E", "rotation": 270, "x": 4, "y": 1}, {"patternId": "smile", "rotation": 0, "x": 4, "y": 2}, {"patternId": "P", "rotation": 180, "x": 5, "y": 2}, {"patternId": "8", "rotation": 270, "x": 6, "y": 2}, {"patternId": "smile", "rotation": 180, "x": 6, "y": 3}, {"patternId": "P", "rotation": 270, "x": 5, "y": 3}], "slot_sequence": ["FRONT", "RIGHT", "BACK", "BOTTOM", "LEFT", "BACK", "TOP", "FRONT", "RIGHT", "TOP"], "required_slots": ["FRONT", "RIGHT", "BACK", "BOTTOM", "LEFT", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "P", "rotation": 270}, "BOTTOM": {"patternId": "E", "rotation": 270}, "FRONT": {"patternId": "8", "rotation": 0}, "BACK": {"patternId": "smile", "rotation": 90}, "LEFT": {"patternId": "E", "rotation": 270}, "RIGHT": {"patternId": "smile", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "P", "rotation": 270}, "BOTTOM": {"patternId": "E", "rotation": 270}, "FRONT": {"patternId": "8", "rotation": 0}, "BACK": {"patternId": "smile", "rotation": 90}, "LEFT": {"patternId": "E", "rotation": 270}, "RIGHT": {"patternId": "smile", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C466\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> E -> N -> E -> S -> E -> E -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=8, rotation=0, flipVertical=true\n- step 2: patternId=smile, rotation=270, flipVertical=true\n- step 3: patternId=smile, rotation=270, flipVertical=true\n- step 4: patternId=E, rotation=90, flipVertical=true\n- step 5: patternId=E, rotation=270, flipVertical=true\n- step 6: patternId=smile, rotation=0, flipVertical=true\n- step 7: patternId=P, rotation=180, flipVertical=true\n- step 8: patternId=8, rotation=270, flipVertical=true\n- step 9: patternId=smile, rotation=180, flipVertical=true\n- step 10: patternId=P, rotation=270, flipVertical=true\n- allowed patternId values for this task: 8, smile, E, P, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C466"} +{"sample_id": "C467", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> E -> S -> N -> S -> N -> E -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "E", "S", "N", "S", "N", "E", "N", "N"], "observed_path_faces": [{"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C467_path_sequence.png"}, "metadata": {"level_id": 467, "name": "Reconstruct 467", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-467.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["2", "A", "2", "arrow_left", "D", "H"], "start_x": 1, "start_y": 4, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "2", "rotation": 90}, "BOTTOM": {"patternId": "H", "rotation": 180}, "FRONT": {"patternId": "A", "rotation": 180}, "BACK": {"patternId": "arrow_left", "rotation": 90}, "LEFT": {"patternId": "D", "rotation": 0}, "RIGHT": {"patternId": "2", "rotation": 90}}, "bottom_faces": [{"patternId": "H", "rotation": 180, "x": 1, "y": 4}, {"patternId": "arrow_left", "rotation": 270, "x": 1, "y": 3}, {"patternId": "2", "rotation": 270, "x": 2, "y": 3}, {"patternId": "A", "rotation": 0, "x": 3, "y": 3}, {"patternId": "H", "rotation": 0, "x": 3, "y": 4}, {"patternId": "A", "rotation": 0, "x": 3, "y": 3}, {"patternId": "H", "rotation": 0, "x": 3, "y": 4}, {"patternId": "A", "rotation": 0, "x": 3, "y": 3}, {"patternId": "D", "rotation": 180, "x": 4, "y": 3}, {"patternId": "2", "rotation": 180, "x": 4, "y": 2}, {"patternId": "2", "rotation": 90, "x": 4, "y": 1}], "slot_sequence": ["BACK", "RIGHT", "FRONT", "BOTTOM", "FRONT", "BOTTOM", "FRONT", "LEFT", "TOP", "RIGHT"], "required_slots": ["BACK", "RIGHT", "FRONT", "BOTTOM", "LEFT", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "2", "rotation": 90}, "BOTTOM": {"patternId": "H", "rotation": 180}, "FRONT": {"patternId": "A", "rotation": 180}, "BACK": {"patternId": "arrow_left", "rotation": 270}, "LEFT": {"patternId": "D", "rotation": 90}, "RIGHT": {"patternId": "2", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "2", "rotation": 90}, "BOTTOM": {"patternId": "H", "rotation": 180}, "FRONT": {"patternId": "A", "rotation": 180}, "BACK": {"patternId": "arrow_left", "rotation": 270}, "LEFT": {"patternId": "D", "rotation": 90}, "RIGHT": {"patternId": "2", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C467\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> E -> S -> N -> S -> N -> E -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_left, rotation=270, flipVertical=true\n- step 2: patternId=2, rotation=270, flipVertical=true\n- step 3: patternId=A, rotation=0, flipVertical=true\n- step 4: patternId=H, rotation=0, flipVertical=true\n- step 5: patternId=A, rotation=0, flipVertical=true\n- step 6: patternId=H, rotation=0, flipVertical=true\n- step 7: patternId=A, rotation=0, flipVertical=true\n- step 8: patternId=D, rotation=180, flipVertical=true\n- step 9: patternId=2, rotation=180, flipVertical=true\n- step 10: patternId=2, rotation=90, flipVertical=true\n- allowed patternId values for this task: arrow_left, 2, A, H, D, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C467"} +{"sample_id": "C468", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> S -> W -> W -> S -> E -> E -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "S", "W", "W", "S", "E", "E", "N", "E"], "observed_path_faces": [{"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C468_path_sequence.png"}, "metadata": {"level_id": 468, "name": "Reconstruct 468", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-468.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["circle", "3", "2", "V", "arrow_down", "4"], "start_x": 1, "start_y": 1, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "circle", "rotation": 270}, "BOTTOM": {"patternId": "4", "rotation": 0}, "FRONT": {"patternId": "3", "rotation": 180}, "BACK": {"patternId": "V", "rotation": 180}, "LEFT": {"patternId": "arrow_down", "rotation": 270}, "RIGHT": {"patternId": "2", "rotation": 180}}, "bottom_faces": [{"patternId": "4", "rotation": 0, "x": 1, "y": 1}, {"patternId": "2", "rotation": 270, "x": 2, "y": 1}, {"patternId": "circle", "rotation": 90, "x": 3, "y": 1}, {"patternId": "3", "rotation": 0, "x": 3, "y": 2}, {"patternId": "2", "rotation": 0, "x": 2, "y": 2}, {"patternId": "V", "rotation": 0, "x": 1, "y": 2}, {"patternId": "4", "rotation": 0, "x": 1, "y": 3}, {"patternId": "2", "rotation": 270, "x": 2, "y": 3}, {"patternId": "circle", "rotation": 90, "x": 3, "y": 3}, {"patternId": "V", "rotation": 180, "x": 3, "y": 2}, {"patternId": "arrow_down", "rotation": 270, "x": 4, "y": 2}], "slot_sequence": ["RIGHT", "TOP", "FRONT", "RIGHT", "BACK", "BOTTOM", "RIGHT", "TOP", "BACK", "LEFT"], "required_slots": ["RIGHT", "TOP", "FRONT", "BACK", "BOTTOM", "LEFT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "circle", "rotation": 270}, "BOTTOM": {"patternId": "4", "rotation": 0}, "FRONT": {"patternId": "3", "rotation": 180}, "BACK": {"patternId": "V", "rotation": 0}, "LEFT": {"patternId": "arrow_down", "rotation": 0}, "RIGHT": {"patternId": "2", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 270}, "BOTTOM": {"patternId": "4", "rotation": 0}, "FRONT": {"patternId": "3", "rotation": 180}, "BACK": {"patternId": "V", "rotation": 0}, "LEFT": {"patternId": "arrow_down", "rotation": 0}, "RIGHT": {"patternId": "2", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C468\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> S -> W -> W -> S -> E -> E -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=2, rotation=270, flipVertical=true\n- step 2: patternId=circle, rotation=90, flipVertical=true\n- step 3: patternId=3, rotation=0, flipVertical=true\n- step 4: patternId=2, rotation=0, flipVertical=true\n- step 5: patternId=V, rotation=0, flipVertical=true\n- step 6: patternId=4, rotation=0, flipVertical=true\n- step 7: patternId=2, rotation=270, flipVertical=true\n- step 8: patternId=circle, rotation=90, flipVertical=true\n- step 9: patternId=V, rotation=180, flipVertical=true\n- step 10: patternId=arrow_down, rotation=270, flipVertical=true\n- allowed patternId values for this task: 2, circle, 3, V, 4, arrow_down, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C468"} +{"sample_id": "C469", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> S -> W -> N -> E -> E -> N -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "S", "W", "N", "E", "E", "N", "E", "E"], "observed_path_faces": [{"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C469_path_sequence.png"}, "metadata": {"level_id": 469, "name": "Reconstruct 469", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-469.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["smile", "O", "Z", "7", "N", "G"], "start_x": 3, "start_y": 1, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "smile", "rotation": 180}, "BOTTOM": {"patternId": "G", "rotation": 0}, "FRONT": {"patternId": "O", "rotation": 270}, "BACK": {"patternId": "7", "rotation": 0}, "LEFT": {"patternId": "N", "rotation": 90}, "RIGHT": {"patternId": "Z", "rotation": 180}}, "bottom_faces": [{"patternId": "G", "rotation": 0, "x": 3, "y": 1}, {"patternId": "O", "rotation": 270, "x": 3, "y": 2}, {"patternId": "N", "rotation": 90, "x": 2, "y": 2}, {"patternId": "smile", "rotation": 90, "x": 2, "y": 3}, {"patternId": "7", "rotation": 90, "x": 1, "y": 3}, {"patternId": "N", "rotation": 180, "x": 1, "y": 2}, {"patternId": "smile", "rotation": 180, "x": 2, "y": 2}, {"patternId": "Z", "rotation": 90, "x": 3, "y": 2}, {"patternId": "O", "rotation": 180, "x": 3, "y": 1}, {"patternId": "G", "rotation": 270, "x": 4, "y": 1}, {"patternId": "7", "rotation": 90, "x": 5, "y": 1}], "slot_sequence": ["FRONT", "LEFT", "TOP", "BACK", "LEFT", "TOP", "RIGHT", "FRONT", "BOTTOM", "BACK"], "required_slots": ["FRONT", "LEFT", "TOP", "BACK", "RIGHT", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "smile", "rotation": 180}, "BOTTOM": {"patternId": "G", "rotation": 0}, "FRONT": {"patternId": "O", "rotation": 270}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "N", "rotation": 180}, "RIGHT": {"patternId": "Z", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 180}, "BOTTOM": {"patternId": "G", "rotation": 0}, "FRONT": {"patternId": "O", "rotation": 270}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "N", "rotation": 180}, "RIGHT": {"patternId": "Z", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C469\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> S -> W -> N -> E -> E -> N -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=O, rotation=270, flipVertical=true\n- step 2: patternId=N, rotation=90, flipVertical=true\n- step 3: patternId=smile, rotation=90, flipVertical=true\n- step 4: patternId=7, rotation=90, flipVertical=true\n- step 5: patternId=N, rotation=180, flipVertical=true\n- step 6: patternId=smile, rotation=180, flipVertical=true\n- step 7: patternId=Z, rotation=90, flipVertical=true\n- step 8: patternId=O, rotation=180, flipVertical=true\n- step 9: patternId=G, rotation=270, flipVertical=true\n- step 10: patternId=7, rotation=90, flipVertical=true\n- allowed patternId values for this task: O, N, smile, 7, Z, G, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C469"} +{"sample_id": "C470", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> E -> N -> W -> S -> E -> S -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "E", "N", "W", "S", "E", "S", "W", "W"], "observed_path_faces": [{"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C470_path_sequence.png"}, "metadata": {"level_id": 470, "name": "Reconstruct 470", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-470.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["L", "heart", "circle", "A", "5", "arrow_down"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "L", "rotation": 180}, "BOTTOM": {"patternId": "arrow_down", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "A", "rotation": 270}, "LEFT": {"patternId": "5", "rotation": 90}, "RIGHT": {"patternId": "circle", "rotation": 90}}, "bottom_faces": [{"patternId": "arrow_down", "rotation": 0, "x": 1, "y": 1}, {"patternId": "heart", "rotation": 270, "x": 1, "y": 2}, {"patternId": "circle", "rotation": 90, "x": 2, "y": 2}, {"patternId": "A", "rotation": 270, "x": 3, "y": 2}, {"patternId": "arrow_down", "rotation": 180, "x": 3, "y": 1}, {"patternId": "circle", "rotation": 0, "x": 2, "y": 1}, {"patternId": "A", "rotation": 180, "x": 2, "y": 2}, {"patternId": "arrow_down", "rotation": 90, "x": 3, "y": 2}, {"patternId": "5", "rotation": 90, "x": 3, "y": 3}, {"patternId": "A", "rotation": 270, "x": 2, "y": 3}, {"patternId": "circle", "rotation": 90, "x": 1, "y": 3}], "slot_sequence": ["FRONT", "RIGHT", "BACK", "BOTTOM", "RIGHT", "BACK", "BOTTOM", "LEFT", "BACK", "RIGHT"], "required_slots": ["FRONT", "RIGHT", "BACK", "BOTTOM", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_down", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "A", "rotation": 90}, "LEFT": {"patternId": "5", "rotation": 180}, "RIGHT": {"patternId": "circle", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_down", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "A", "rotation": 90}, "LEFT": {"patternId": "5", "rotation": 180}, "RIGHT": {"patternId": "circle", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C470\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> E -> N -> W -> S -> E -> S -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=heart, rotation=270, flipVertical=true\n- step 2: patternId=circle, rotation=90, flipVertical=true\n- step 3: patternId=A, rotation=270, flipVertical=true\n- step 4: patternId=arrow_down, rotation=180, flipVertical=true\n- step 5: patternId=circle, rotation=0, flipVertical=true\n- step 6: patternId=A, rotation=180, flipVertical=true\n- step 7: patternId=arrow_down, rotation=90, flipVertical=true\n- step 8: patternId=5, rotation=90, flipVertical=true\n- step 9: patternId=A, rotation=270, flipVertical=true\n- step 10: patternId=circle, rotation=90, flipVertical=true\n- allowed patternId values for this task: heart, circle, A, arrow_down, 5, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C470"} +{"sample_id": "C471", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> E -> S -> E -> N -> W -> W -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "E", "S", "E", "N", "W", "W", "E", "N"], "observed_path_faces": [{"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C471_path_sequence.png"}, "metadata": {"level_id": 471, "name": "Reconstruct 471", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-471.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["H", "U", "triangle", "W", "B", "Q"], "start_x": 1, "start_y": 3, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "H", "rotation": 180}, "BOTTOM": {"patternId": "Q", "rotation": 90}, "FRONT": {"patternId": "U", "rotation": 180}, "BACK": {"patternId": "W", "rotation": 180}, "LEFT": {"patternId": "B", "rotation": 90}, "RIGHT": {"patternId": "triangle", "rotation": 180}}, "bottom_faces": [{"patternId": "Q", "rotation": 90, "x": 1, "y": 3}, {"patternId": "triangle", "rotation": 270, "x": 2, "y": 3}, {"patternId": "W", "rotation": 270, "x": 2, "y": 2}, {"patternId": "H", "rotation": 90, "x": 3, "y": 2}, {"patternId": "triangle", "rotation": 0, "x": 3, "y": 3}, {"patternId": "U", "rotation": 0, "x": 4, "y": 3}, {"patternId": "H", "rotation": 0, "x": 4, "y": 2}, {"patternId": "triangle", "rotation": 270, "x": 3, "y": 2}, {"patternId": "Q", "rotation": 90, "x": 2, "y": 2}, {"patternId": "triangle", "rotation": 270, "x": 3, "y": 2}, {"patternId": "W", "rotation": 270, "x": 3, "y": 1}], "slot_sequence": ["RIGHT", "BACK", "TOP", "RIGHT", "FRONT", "TOP", "RIGHT", "BOTTOM", "RIGHT", "BACK"], "required_slots": ["RIGHT", "BACK", "TOP", "FRONT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "H", "rotation": 180}, "BOTTOM": {"patternId": "Q", "rotation": 90}, "FRONT": {"patternId": "U", "rotation": 180}, "BACK": {"patternId": "W", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "triangle", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "H", "rotation": 180}, "BOTTOM": {"patternId": "Q", "rotation": 90}, "FRONT": {"patternId": "U", "rotation": 180}, "BACK": {"patternId": "W", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "triangle", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C471\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> E -> S -> E -> N -> W -> W -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=triangle, rotation=270, flipVertical=true\n- step 2: patternId=W, rotation=270, flipVertical=true\n- step 3: patternId=H, rotation=90, flipVertical=true\n- step 4: patternId=triangle, rotation=0, flipVertical=true\n- step 5: patternId=U, rotation=0, flipVertical=true\n- step 6: patternId=H, rotation=0, flipVertical=true\n- step 7: patternId=triangle, rotation=270, flipVertical=true\n- step 8: patternId=Q, rotation=90, flipVertical=true\n- step 9: patternId=triangle, rotation=270, flipVertical=true\n- step 10: patternId=W, rotation=270, flipVertical=true\n- allowed patternId values for this task: triangle, W, H, U, Q, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C471"} +{"sample_id": "C472", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> S -> W -> N -> N -> W -> N -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "S", "W", "N", "N", "W", "N", "E", "N"], "observed_path_faces": [{"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C472_path_sequence.png"}, "metadata": {"level_id": 472, "name": "Reconstruct 472", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-472.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["5", "H", "O", "M", "G", "G"], "start_x": 4, "start_y": 5, "grid_width": 6, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "5", "rotation": 180}, "BOTTOM": {"patternId": "G", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 270}, "LEFT": {"patternId": "G", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 180}}, "bottom_faces": [{"patternId": "G", "rotation": 0, "x": 4, "y": 5}, {"patternId": "M", "rotation": 90, "x": 4, "y": 4}, {"patternId": "G", "rotation": 180, "x": 3, "y": 4}, {"patternId": "G", "rotation": 270, "x": 3, "y": 5}, {"patternId": "H", "rotation": 270, "x": 2, "y": 5}, {"patternId": "G", "rotation": 270, "x": 2, "y": 4}, {"patternId": "M", "rotation": 180, "x": 2, "y": 3}, {"patternId": "5", "rotation": 270, "x": 1, "y": 3}, {"patternId": "O", "rotation": 180, "x": 1, "y": 2}, {"patternId": "M", "rotation": 270, "x": 2, "y": 2}, {"patternId": "G", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["BACK", "LEFT", "BOTTOM", "FRONT", "LEFT", "BACK", "TOP", "RIGHT", "BACK", "BOTTOM"], "required_slots": ["BACK", "LEFT", "BOTTOM", "FRONT", "TOP", "RIGHT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "5", "rotation": 180}, "BOTTOM": {"patternId": "G", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "G", "rotation": 90}, "RIGHT": {"patternId": "O", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "5", "rotation": 180}, "BOTTOM": {"patternId": "G", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "G", "rotation": 90}, "RIGHT": {"patternId": "O", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C472\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> S -> W -> N -> N -> W -> N -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=M, rotation=90, flipVertical=true\n- step 2: patternId=G, rotation=180, flipVertical=true\n- step 3: patternId=G, rotation=270, flipVertical=true\n- step 4: patternId=H, rotation=270, flipVertical=true\n- step 5: patternId=G, rotation=270, flipVertical=true\n- step 6: patternId=M, rotation=180, flipVertical=true\n- step 7: patternId=5, rotation=270, flipVertical=true\n- step 8: patternId=O, rotation=180, flipVertical=true\n- step 9: patternId=M, rotation=270, flipVertical=true\n- step 10: patternId=G, rotation=180, flipVertical=true\n- allowed patternId values for this task: M, G, H, 5, O, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C472"} +{"sample_id": "C473", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> E -> S -> N -> S -> E -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "W", "E", "S", "N", "S", "E", "E", "E"], "observed_path_faces": [{"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C473_path_sequence.png"}, "metadata": {"level_id": 473, "name": "Reconstruct 473", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-473.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["I", "X", "Y", "M", "heart", "triangle"], "start_x": 1, "start_y": 1, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "I", "rotation": 180}, "BOTTOM": {"patternId": "triangle", "rotation": 270}, "FRONT": {"patternId": "X", "rotation": 270}, "BACK": {"patternId": "M", "rotation": 270}, "LEFT": {"patternId": "heart", "rotation": 0}, "RIGHT": {"patternId": "Y", "rotation": 90}}, "bottom_faces": [{"patternId": "triangle", "rotation": 270, "x": 1, "y": 1}, {"patternId": "Y", "rotation": 180, "x": 2, "y": 1}, {"patternId": "X", "rotation": 0, "x": 2, "y": 2}, {"patternId": "triangle", "rotation": 0, "x": 1, "y": 2}, {"patternId": "X", "rotation": 0, "x": 2, "y": 2}, {"patternId": "heart", "rotation": 90, "x": 2, "y": 3}, {"patternId": "X", "rotation": 0, "x": 2, "y": 2}, {"patternId": "heart", "rotation": 90, "x": 2, "y": 3}, {"patternId": "I", "rotation": 180, "x": 3, "y": 3}, {"patternId": "Y", "rotation": 0, "x": 4, "y": 3}, {"patternId": "triangle", "rotation": 90, "x": 5, "y": 3}], "slot_sequence": ["RIGHT", "FRONT", "BOTTOM", "FRONT", "LEFT", "FRONT", "LEFT", "TOP", "RIGHT", "BOTTOM"], "required_slots": ["RIGHT", "FRONT", "BOTTOM", "LEFT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "I", "rotation": 180}, "BOTTOM": {"patternId": "triangle", "rotation": 270}, "FRONT": {"patternId": "X", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 90}, "RIGHT": {"patternId": "Y", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 180}, "BOTTOM": {"patternId": "triangle", "rotation": 270}, "FRONT": {"patternId": "X", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 90}, "RIGHT": {"patternId": "Y", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C473\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> E -> S -> N -> S -> E -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Y, rotation=180, flipVertical=true\n- step 2: patternId=X, rotation=0, flipVertical=true\n- step 3: patternId=triangle, rotation=0, flipVertical=true\n- step 4: patternId=X, rotation=0, flipVertical=true\n- step 5: patternId=heart, rotation=90, flipVertical=true\n- step 6: patternId=X, rotation=0, flipVertical=true\n- step 7: patternId=heart, rotation=90, flipVertical=true\n- step 8: patternId=I, rotation=180, flipVertical=true\n- step 9: patternId=Y, rotation=0, flipVertical=true\n- step 10: patternId=triangle, rotation=90, flipVertical=true\n- allowed patternId values for this task: Y, X, triangle, heart, I, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C473"} +{"sample_id": "C474", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> E -> E -> N -> N -> W -> N -> S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "E", "E", "N", "N", "W", "N", "S", "N"], "observed_path_faces": [{"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C474_path_sequence.png"}, "metadata": {"level_id": 474, "name": "Reconstruct 474", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-474.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_right", "Z", "L", "plus", "N", "triangle"], "start_x": 2, "start_y": 5, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "arrow_right", "rotation": 270}, "BOTTOM": {"patternId": "triangle", "rotation": 0}, "FRONT": {"patternId": "Z", "rotation": 90}, "BACK": {"patternId": "plus", "rotation": 0}, "LEFT": {"patternId": "N", "rotation": 90}, "RIGHT": {"patternId": "L", "rotation": 270}}, "bottom_faces": [{"patternId": "triangle", "rotation": 0, "x": 2, "y": 5}, {"patternId": "plus", "rotation": 180, "x": 2, "y": 4}, {"patternId": "N", "rotation": 270, "x": 1, "y": 4}, {"patternId": "plus", "rotation": 180, "x": 2, "y": 4}, {"patternId": "L", "rotation": 90, "x": 3, "y": 4}, {"patternId": "arrow_right", "rotation": 180, "x": 3, "y": 3}, {"patternId": "N", "rotation": 90, "x": 3, "y": 2}, {"patternId": "plus", "rotation": 0, "x": 2, "y": 2}, {"patternId": "triangle", "rotation": 180, "x": 2, "y": 1}, {"patternId": "plus", "rotation": 0, "x": 2, "y": 2}, {"patternId": "triangle", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["BACK", "LEFT", "BACK", "RIGHT", "TOP", "LEFT", "BACK", "BOTTOM", "BACK", "BOTTOM"], "required_slots": ["BACK", "LEFT", "RIGHT", "TOP", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "arrow_right", "rotation": 270}, "BOTTOM": {"patternId": "triangle", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "plus", "rotation": 180}, "LEFT": {"patternId": "N", "rotation": 180}, "RIGHT": {"patternId": "L", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "arrow_right", "rotation": 270}, "BOTTOM": {"patternId": "triangle", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "plus", "rotation": 180}, "LEFT": {"patternId": "N", "rotation": 180}, "RIGHT": {"patternId": "L", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C474\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> E -> E -> N -> N -> W -> N -> S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=plus, rotation=180, flipVertical=true\n- step 2: patternId=N, rotation=270, flipVertical=true\n- step 3: patternId=plus, rotation=180, flipVertical=true\n- step 4: patternId=L, rotation=90, flipVertical=true\n- step 5: patternId=arrow_right, rotation=180, flipVertical=true\n- step 6: patternId=N, rotation=90, flipVertical=true\n- step 7: patternId=plus, rotation=0, flipVertical=true\n- step 8: patternId=triangle, rotation=180, flipVertical=true\n- step 9: patternId=plus, rotation=0, flipVertical=true\n- step 10: patternId=triangle, rotation=180, flipVertical=true\n- allowed patternId values for this task: plus, N, L, arrow_right, triangle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C474"} +{"sample_id": "C475", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> W -> N -> N -> N -> E -> N -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "S", "W", "N", "N", "N", "E", "N", "N", "E"], "observed_path_faces": [{"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C475_path_sequence.png"}, "metadata": {"level_id": 475, "name": "Reconstruct 475", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-475.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["C", "9", "arrow_right", "R", "1", "triangle"], "start_x": 2, "start_y": 4, "grid_width": 5, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "C", "rotation": 180}, "BOTTOM": {"patternId": "triangle", "rotation": 90}, "FRONT": {"patternId": "9", "rotation": 270}, "BACK": {"patternId": "R", "rotation": 0}, "LEFT": {"patternId": "1", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}}, "bottom_faces": [{"patternId": "triangle", "rotation": 90, "x": 2, "y": 4}, {"patternId": "9", "rotation": 270, "x": 2, "y": 5}, {"patternId": "C", "rotation": 180, "x": 2, "y": 6}, {"patternId": "1", "rotation": 90, "x": 1, "y": 6}, {"patternId": "9", "rotation": 0, "x": 1, "y": 5}, {"patternId": "arrow_right", "rotation": 0, "x": 1, "y": 4}, {"patternId": "R", "rotation": 90, "x": 1, "y": 3}, {"patternId": "C", "rotation": 90, "x": 2, "y": 3}, {"patternId": "1", "rotation": 0, "x": 2, "y": 2}, {"patternId": "triangle", "rotation": 180, "x": 2, "y": 1}, {"patternId": "9", "rotation": 0, "x": 3, "y": 1}], "slot_sequence": ["FRONT", "TOP", "LEFT", "FRONT", "RIGHT", "BACK", "TOP", "LEFT", "BOTTOM", "FRONT"], "required_slots": ["FRONT", "TOP", "LEFT", "RIGHT", "BACK", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "C", "rotation": 180}, "BOTTOM": {"patternId": "triangle", "rotation": 90}, "FRONT": {"patternId": "9", "rotation": 270}, "BACK": {"patternId": "R", "rotation": 180}, "LEFT": {"patternId": "1", "rotation": 90}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "C", "rotation": 180}, "BOTTOM": {"patternId": "triangle", "rotation": 90}, "FRONT": {"patternId": "9", "rotation": 270}, "BACK": {"patternId": "R", "rotation": 180}, "LEFT": {"patternId": "1", "rotation": 90}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C475\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> W -> N -> N -> N -> E -> N -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=9, rotation=270, flipVertical=true\n- step 2: patternId=C, rotation=180, flipVertical=true\n- step 3: patternId=1, rotation=90, flipVertical=true\n- step 4: patternId=9, rotation=0, flipVertical=true\n- step 5: patternId=arrow_right, rotation=0, flipVertical=true\n- step 6: patternId=R, rotation=90, flipVertical=true\n- step 7: patternId=C, rotation=90, flipVertical=true\n- step 8: patternId=1, rotation=0, flipVertical=true\n- step 9: patternId=triangle, rotation=180, flipVertical=true\n- step 10: patternId=9, rotation=0, flipVertical=true\n- allowed patternId values for this task: 9, C, 1, arrow_right, R, triangle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C475"} +{"sample_id": "C476", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> S -> W -> S -> N -> N -> W -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "S", "W", "S", "N", "N", "W", "N", "N"], "observed_path_faces": [{"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C476_path_sequence.png"}, "metadata": {"level_id": 476, "name": "Reconstruct 476", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-476.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["5", "F", "Q", "circle", "I", "9"], "start_x": 5, "start_y": 3, "grid_width": 7, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "9", "rotation": 0}, "FRONT": {"patternId": "F", "rotation": 90}, "BACK": {"patternId": "circle", "rotation": 0}, "LEFT": {"patternId": "I", "rotation": 180}, "RIGHT": {"patternId": "Q", "rotation": 0}}, "bottom_faces": [{"patternId": "9", "rotation": 0, "x": 5, "y": 3}, {"patternId": "I", "rotation": 90, "x": 4, "y": 3}, {"patternId": "5", "rotation": 270, "x": 3, "y": 3}, {"patternId": "F", "rotation": 270, "x": 3, "y": 4}, {"patternId": "Q", "rotation": 180, "x": 2, "y": 4}, {"patternId": "9", "rotation": 90, "x": 2, "y": 5}, {"patternId": "Q", "rotation": 180, "x": 2, "y": 4}, {"patternId": "5", "rotation": 0, "x": 2, "y": 3}, {"patternId": "circle", "rotation": 90, "x": 1, "y": 3}, {"patternId": "I", "rotation": 270, "x": 1, "y": 2}, {"patternId": "F", "rotation": 180, "x": 1, "y": 1}], "slot_sequence": ["LEFT", "TOP", "FRONT", "RIGHT", "BOTTOM", "RIGHT", "TOP", "BACK", "LEFT", "FRONT"], "required_slots": ["LEFT", "TOP", "FRONT", "RIGHT", "BOTTOM", "BACK"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "9", "rotation": 0}, "FRONT": {"patternId": "F", "rotation": 90}, "BACK": {"patternId": "circle", "rotation": 180}, "LEFT": {"patternId": "I", "rotation": 270}, "RIGHT": {"patternId": "Q", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "9", "rotation": 0}, "FRONT": {"patternId": "F", "rotation": 90}, "BACK": {"patternId": "circle", "rotation": 180}, "LEFT": {"patternId": "I", "rotation": 270}, "RIGHT": {"patternId": "Q", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C476\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> S -> W -> S -> N -> N -> W -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=I, rotation=90, flipVertical=true\n- step 2: patternId=5, rotation=270, flipVertical=true\n- step 3: patternId=F, rotation=270, flipVertical=true\n- step 4: patternId=Q, rotation=180, flipVertical=true\n- step 5: patternId=9, rotation=90, flipVertical=true\n- step 6: patternId=Q, rotation=180, flipVertical=true\n- step 7: patternId=5, rotation=0, flipVertical=true\n- step 8: patternId=circle, rotation=90, flipVertical=true\n- step 9: patternId=I, rotation=270, flipVertical=true\n- step 10: patternId=F, rotation=180, flipVertical=true\n- allowed patternId values for this task: I, 5, F, Q, 9, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C476"} +{"sample_id": "C477", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> N -> W -> E -> N -> E -> E -> E -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "N", "W", "E", "N", "E", "E", "E", "W"], "observed_path_faces": [{"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C477_path_sequence.png"}, "metadata": {"level_id": 477, "name": "Reconstruct 477", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-477.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["C", "I", "O", "C", "D", "6"], "start_x": 4, "start_y": 3, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "C", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "I", "rotation": 90}, "BACK": {"patternId": "C", "rotation": 270}, "LEFT": {"patternId": "D", "rotation": 180}, "RIGHT": {"patternId": "O", "rotation": 0}}, "bottom_faces": [{"patternId": "6", "rotation": 180, "x": 4, "y": 3}, {"patternId": "D", "rotation": 90, "x": 3, "y": 3}, {"patternId": "C", "rotation": 180, "x": 2, "y": 3}, {"patternId": "C", "rotation": 270, "x": 2, "y": 2}, {"patternId": "O", "rotation": 0, "x": 1, "y": 2}, {"patternId": "C", "rotation": 270, "x": 2, "y": 2}, {"patternId": "6", "rotation": 0, "x": 2, "y": 1}, {"patternId": "D", "rotation": 270, "x": 3, "y": 1}, {"patternId": "C", "rotation": 0, "x": 4, "y": 1}, {"patternId": "O", "rotation": 270, "x": 5, "y": 1}, {"patternId": "C", "rotation": 0, "x": 4, "y": 1}], "slot_sequence": ["LEFT", "TOP", "BACK", "RIGHT", "BACK", "BOTTOM", "LEFT", "TOP", "RIGHT", "TOP"], "required_slots": ["LEFT", "TOP", "BACK", "RIGHT", "BOTTOM"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "C", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "C", "rotation": 90}, "LEFT": {"patternId": "D", "rotation": 270}, "RIGHT": {"patternId": "O", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "C", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "C", "rotation": 90}, "LEFT": {"patternId": "D", "rotation": 270}, "RIGHT": {"patternId": "O", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C477\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> N -> W -> E -> N -> E -> E -> E -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=D, rotation=90, flipVertical=true\n- step 2: patternId=C, rotation=180, flipVertical=true\n- step 3: patternId=C, rotation=270, flipVertical=true\n- step 4: patternId=O, rotation=0, flipVertical=true\n- step 5: patternId=C, rotation=270, flipVertical=true\n- step 6: patternId=6, rotation=0, flipVertical=true\n- step 7: patternId=D, rotation=270, flipVertical=true\n- step 8: patternId=C, rotation=0, flipVertical=true\n- step 9: patternId=O, rotation=270, flipVertical=true\n- step 10: patternId=C, rotation=0, flipVertical=true\n- allowed patternId values for this task: D, C, O, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C477"} +{"sample_id": "C478", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> E -> S -> S -> W -> W -> S -> E -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "E", "S", "S", "W", "W", "S", "E", "W"], "observed_path_faces": [{"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C478_path_sequence.png"}, "metadata": {"level_id": 478, "name": "Reconstruct 478", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-478.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["triangle", "C", "O", "Y", "D", "E"], "start_x": 1, "start_y": 1, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "triangle", "rotation": 0}, "BOTTOM": {"patternId": "E", "rotation": 180}, "FRONT": {"patternId": "C", "rotation": 0}, "BACK": {"patternId": "Y", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 0}}, "bottom_faces": [{"patternId": "E", "rotation": 180, "x": 1, "y": 1}, {"patternId": "O", "rotation": 90, "x": 2, "y": 1}, {"patternId": "triangle", "rotation": 180, "x": 3, "y": 1}, {"patternId": "D", "rotation": 270, "x": 4, "y": 1}, {"patternId": "C", "rotation": 270, "x": 4, "y": 2}, {"patternId": "O", "rotation": 270, "x": 4, "y": 3}, {"patternId": "triangle", "rotation": 0, "x": 3, "y": 3}, {"patternId": "D", "rotation": 90, "x": 2, "y": 3}, {"patternId": "Y", "rotation": 90, "x": 2, "y": 4}, {"patternId": "triangle", "rotation": 270, "x": 3, "y": 4}, {"patternId": "Y", "rotation": 90, "x": 2, "y": 4}], "slot_sequence": ["RIGHT", "TOP", "LEFT", "FRONT", "RIGHT", "TOP", "LEFT", "BACK", "TOP", "BACK"], "required_slots": ["RIGHT", "TOP", "LEFT", "FRONT", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "triangle", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "C", "rotation": 0}, "BACK": {"patternId": "Y", "rotation": 180}, "LEFT": {"patternId": "D", "rotation": 90}, "RIGHT": {"patternId": "O", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "triangle", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "C", "rotation": 0}, "BACK": {"patternId": "Y", "rotation": 180}, "LEFT": {"patternId": "D", "rotation": 90}, "RIGHT": {"patternId": "O", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C478\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> E -> S -> S -> W -> W -> S -> E -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=O, rotation=90, flipVertical=true\n- step 2: patternId=triangle, rotation=180, flipVertical=true\n- step 3: patternId=D, rotation=270, flipVertical=true\n- step 4: patternId=C, rotation=270, flipVertical=true\n- step 5: patternId=O, rotation=270, flipVertical=true\n- step 6: patternId=triangle, rotation=0, flipVertical=true\n- step 7: patternId=D, rotation=90, flipVertical=true\n- step 8: patternId=Y, rotation=90, flipVertical=true\n- step 9: patternId=triangle, rotation=270, flipVertical=true\n- step 10: patternId=Y, rotation=90, flipVertical=true\n- allowed patternId values for this task: O, triangle, D, C, Y, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C478"} +{"sample_id": "C479", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> E -> S -> N -> W -> W -> W -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "E", "S", "N", "W", "W", "W", "S", "W"], "observed_path_faces": [{"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C479_path_sequence.png"}, "metadata": {"level_id": 479, "name": "Reconstruct 479", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-479.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Z", "Y", "E", "G", "E", "P"], "start_x": 5, "start_y": 1, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "Z", "rotation": 0}, "BOTTOM": {"patternId": "P", "rotation": 90}, "FRONT": {"patternId": "Y", "rotation": 90}, "BACK": {"patternId": "G", "rotation": 0}, "LEFT": {"patternId": "E", "rotation": 270}, "RIGHT": {"patternId": "E", "rotation": 90}}, "bottom_faces": [{"patternId": "P", "rotation": 90, "x": 5, "y": 1}, {"patternId": "Y", "rotation": 90, "x": 5, "y": 2}, {"patternId": "E", "rotation": 270, "x": 4, "y": 2}, {"patternId": "Y", "rotation": 90, "x": 5, "y": 2}, {"patternId": "Z", "rotation": 0, "x": 5, "y": 3}, {"patternId": "Y", "rotation": 90, "x": 5, "y": 2}, {"patternId": "E", "rotation": 270, "x": 4, "y": 2}, {"patternId": "G", "rotation": 0, "x": 3, "y": 2}, {"patternId": "E", "rotation": 90, "x": 2, "y": 2}, {"patternId": "Z", "rotation": 90, "x": 2, "y": 3}, {"patternId": "Y", "rotation": 180, "x": 1, "y": 3}], "slot_sequence": ["FRONT", "LEFT", "FRONT", "TOP", "FRONT", "LEFT", "BACK", "RIGHT", "TOP", "FRONT"], "required_slots": ["FRONT", "LEFT", "TOP", "BACK", "RIGHT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "Z", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "Y", "rotation": 90}, "BACK": {"patternId": "G", "rotation": 180}, "LEFT": {"patternId": "E", "rotation": 0}, "RIGHT": {"patternId": "E", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "Z", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "Y", "rotation": 90}, "BACK": {"patternId": "G", "rotation": 180}, "LEFT": {"patternId": "E", "rotation": 0}, "RIGHT": {"patternId": "E", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C479\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> E -> S -> N -> W -> W -> W -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Y, rotation=90, flipVertical=true\n- step 2: patternId=E, rotation=270, flipVertical=true\n- step 3: patternId=Y, rotation=90, flipVertical=true\n- step 4: patternId=Z, rotation=0, flipVertical=true\n- step 5: patternId=Y, rotation=90, flipVertical=true\n- step 6: patternId=E, rotation=270, flipVertical=true\n- step 7: patternId=G, rotation=0, flipVertical=true\n- step 8: patternId=E, rotation=90, flipVertical=true\n- step 9: patternId=Z, rotation=90, flipVertical=true\n- step 10: patternId=Y, rotation=180, flipVertical=true\n- allowed patternId values for this task: Y, E, Z, G, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C479"} +{"sample_id": "C480", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> W -> E -> S -> E -> W -> N -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "N", "W", "E", "S", "E", "W", "N", "N", "N"], "observed_path_faces": [{"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C480_path_sequence.png"}, "metadata": {"level_id": 480, "name": "Reconstruct 480", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-480.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Q", "E", "diamond", "N", "F", "8"], "start_x": 3, "start_y": 4, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "Q", "rotation": 90}, "BOTTOM": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "E", "rotation": 180}, "BACK": {"patternId": "N", "rotation": 270}, "LEFT": {"patternId": "F", "rotation": 180}, "RIGHT": {"patternId": "diamond", "rotation": 270}}, "bottom_faces": [{"patternId": "8", "rotation": 180, "x": 3, "y": 4}, {"patternId": "F", "rotation": 90, "x": 2, "y": 4}, {"patternId": "N", "rotation": 180, "x": 2, "y": 3}, {"patternId": "Q", "rotation": 180, "x": 1, "y": 3}, {"patternId": "N", "rotation": 180, "x": 2, "y": 3}, {"patternId": "F", "rotation": 90, "x": 2, "y": 4}, {"patternId": "8", "rotation": 180, "x": 3, "y": 4}, {"patternId": "F", "rotation": 90, "x": 2, "y": 4}, {"patternId": "N", "rotation": 180, "x": 2, "y": 3}, {"patternId": "diamond", "rotation": 180, "x": 2, "y": 2}, {"patternId": "E", "rotation": 90, "x": 2, "y": 1}], "slot_sequence": ["LEFT", "BACK", "TOP", "BACK", "LEFT", "BOTTOM", "LEFT", "BACK", "RIGHT", "FRONT"], "required_slots": ["LEFT", "BACK", "TOP", "BOTTOM", "RIGHT", "FRONT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "Q", "rotation": 90}, "BOTTOM": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "E", "rotation": 180}, "BACK": {"patternId": "N", "rotation": 90}, "LEFT": {"patternId": "F", "rotation": 270}, "RIGHT": {"patternId": "diamond", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "Q", "rotation": 90}, "BOTTOM": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "E", "rotation": 180}, "BACK": {"patternId": "N", "rotation": 90}, "LEFT": {"patternId": "F", "rotation": 270}, "RIGHT": {"patternId": "diamond", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C480\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> W -> E -> S -> E -> W -> N -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=F, rotation=90, flipVertical=true\n- step 2: patternId=N, rotation=180, flipVertical=true\n- step 3: patternId=Q, rotation=180, flipVertical=true\n- step 4: patternId=N, rotation=180, flipVertical=true\n- step 5: patternId=F, rotation=90, flipVertical=true\n- step 6: patternId=8, rotation=180, flipVertical=true\n- step 7: patternId=F, rotation=90, flipVertical=true\n- step 8: patternId=N, rotation=180, flipVertical=true\n- step 9: patternId=diamond, rotation=180, flipVertical=true\n- step 10: patternId=E, rotation=90, flipVertical=true\n- allowed patternId values for this task: F, N, Q, 8, diamond, E, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C480"} +{"sample_id": "C481", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> W -> N -> E -> N -> W -> N -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "W", "N", "E", "N", "W", "N", "E", "E"], "observed_path_faces": [{"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C481_path_sequence.png"}, "metadata": {"level_id": 481, "name": "Reconstruct 481", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-481.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["6", "square", "M", "S", "K", "B"], "start_x": 3, "start_y": 5, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "6", "rotation": 180}, "BOTTOM": {"patternId": "B", "rotation": 180}, "FRONT": {"patternId": "square", "rotation": 270}, "BACK": {"patternId": "S", "rotation": 270}, "LEFT": {"patternId": "K", "rotation": 90}, "RIGHT": {"patternId": "M", "rotation": 180}}, "bottom_faces": [{"patternId": "B", "rotation": 180, "x": 3, "y": 5}, {"patternId": "S", "rotation": 90, "x": 3, "y": 4}, {"patternId": "K", "rotation": 270, "x": 2, "y": 4}, {"patternId": "square", "rotation": 90, "x": 1, "y": 4}, {"patternId": "6", "rotation": 0, "x": 1, "y": 3}, {"patternId": "K", "rotation": 0, "x": 2, "y": 3}, {"patternId": "S", "rotation": 180, "x": 2, "y": 2}, {"patternId": "6", "rotation": 270, "x": 1, "y": 2}, {"patternId": "M", "rotation": 180, "x": 1, "y": 1}, {"patternId": "S", "rotation": 270, "x": 2, "y": 1}, {"patternId": "K", "rotation": 90, "x": 3, "y": 1}], "slot_sequence": ["BACK", "LEFT", "FRONT", "TOP", "LEFT", "BACK", "TOP", "RIGHT", "BACK", "LEFT"], "required_slots": ["BACK", "LEFT", "FRONT", "TOP", "RIGHT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "6", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 270}, "BACK": {"patternId": "S", "rotation": 90}, "LEFT": {"patternId": "K", "rotation": 180}, "RIGHT": {"patternId": "M", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 270}, "BACK": {"patternId": "S", "rotation": 90}, "LEFT": {"patternId": "K", "rotation": 180}, "RIGHT": {"patternId": "M", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C481\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> W -> N -> E -> N -> W -> N -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=S, rotation=90, flipVertical=true\n- step 2: patternId=K, rotation=270, flipVertical=true\n- step 3: patternId=square, rotation=90, flipVertical=true\n- step 4: patternId=6, rotation=0, flipVertical=true\n- step 5: patternId=K, rotation=0, flipVertical=true\n- step 6: patternId=S, rotation=180, flipVertical=true\n- step 7: patternId=6, rotation=270, flipVertical=true\n- step 8: patternId=M, rotation=180, flipVertical=true\n- step 9: patternId=S, rotation=270, flipVertical=true\n- step 10: patternId=K, rotation=90, flipVertical=true\n- allowed patternId values for this task: S, K, square, 6, M, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C481"} +{"sample_id": "C482", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> W -> W -> E -> S -> E -> S -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "W", "W", "E", "S", "E", "S", "S", "S"], "observed_path_faces": [{"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C482_path_sequence.png"}, "metadata": {"level_id": 482, "name": "Reconstruct 482", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-482.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["L", "D", "J", "diamond", "1", "diamond"], "start_x": 2, "start_y": 1, "grid_width": 5, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "L", "rotation": 180}, "BOTTOM": {"patternId": "diamond", "rotation": 90}, "FRONT": {"patternId": "D", "rotation": 270}, "BACK": {"patternId": "diamond", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 180}, "RIGHT": {"patternId": "J", "rotation": 270}}, "bottom_faces": [{"patternId": "diamond", "rotation": 90, "x": 2, "y": 1}, {"patternId": "D", "rotation": 270, "x": 2, "y": 2}, {"patternId": "J", "rotation": 270, "x": 3, "y": 2}, {"patternId": "D", "rotation": 270, "x": 2, "y": 2}, {"patternId": "1", "rotation": 180, "x": 1, "y": 2}, {"patternId": "D", "rotation": 270, "x": 2, "y": 2}, {"patternId": "L", "rotation": 180, "x": 2, "y": 3}, {"patternId": "J", "rotation": 180, "x": 3, "y": 3}, {"patternId": "diamond", "rotation": 0, "x": 3, "y": 4}, {"patternId": "1", "rotation": 90, "x": 3, "y": 5}, {"patternId": "D", "rotation": 180, "x": 3, "y": 6}], "slot_sequence": ["FRONT", "RIGHT", "FRONT", "LEFT", "FRONT", "TOP", "RIGHT", "BACK", "LEFT", "FRONT"], "required_slots": ["FRONT", "RIGHT", "LEFT", "TOP", "BACK"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "L", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 270}, "BACK": {"patternId": "diamond", "rotation": 270}, "LEFT": {"patternId": "1", "rotation": 270}, "RIGHT": {"patternId": "J", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "L", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 270}, "BACK": {"patternId": "diamond", "rotation": 270}, "LEFT": {"patternId": "1", "rotation": 270}, "RIGHT": {"patternId": "J", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C482\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> W -> W -> E -> S -> E -> S -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=D, rotation=270, flipVertical=true\n- step 2: patternId=J, rotation=270, flipVertical=true\n- step 3: patternId=D, rotation=270, flipVertical=true\n- step 4: patternId=1, rotation=180, flipVertical=true\n- step 5: patternId=D, rotation=270, flipVertical=true\n- step 6: patternId=L, rotation=180, flipVertical=true\n- step 7: patternId=J, rotation=180, flipVertical=true\n- step 8: patternId=diamond, rotation=0, flipVertical=true\n- step 9: patternId=1, rotation=90, flipVertical=true\n- step 10: patternId=D, rotation=180, flipVertical=true\n- allowed patternId values for this task: D, J, 1, L, diamond, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C482"} +{"sample_id": "C483", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> N -> N -> E -> E -> S -> E -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "N", "N", "E", "E", "S", "E", "S", "S"], "observed_path_faces": [{"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C483_path_sequence.png"}, "metadata": {"level_id": 483, "name": "Reconstruct 483", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-483.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["star", "F", "9", "P", "arrow_down", "square"], "start_x": 2, "start_y": 4, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "star", "rotation": 0}, "BOTTOM": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "F", "rotation": 270}, "BACK": {"patternId": "P", "rotation": 0}, "LEFT": {"patternId": "arrow_down", "rotation": 90}, "RIGHT": {"patternId": "9", "rotation": 90}}, "bottom_faces": [{"patternId": "square", "rotation": 90, "x": 2, "y": 4}, {"patternId": "P", "rotation": 180, "x": 2, "y": 3}, {"patternId": "arrow_down", "rotation": 270, "x": 1, "y": 3}, {"patternId": "star", "rotation": 90, "x": 1, "y": 2}, {"patternId": "9", "rotation": 90, "x": 1, "y": 1}, {"patternId": "P", "rotation": 0, "x": 2, "y": 1}, {"patternId": "arrow_down", "rotation": 90, "x": 3, "y": 1}, {"patternId": "star", "rotation": 270, "x": 3, "y": 2}, {"patternId": "F", "rotation": 180, "x": 4, "y": 2}, {"patternId": "9", "rotation": 0, "x": 4, "y": 3}, {"patternId": "P", "rotation": 270, "x": 4, "y": 4}], "slot_sequence": ["BACK", "LEFT", "TOP", "RIGHT", "BACK", "LEFT", "TOP", "FRONT", "RIGHT", "BACK"], "required_slots": ["BACK", "LEFT", "TOP", "RIGHT", "FRONT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "star", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "F", "rotation": 270}, "BACK": {"patternId": "P", "rotation": 180}, "LEFT": {"patternId": "arrow_down", "rotation": 180}, "RIGHT": {"patternId": "9", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "F", "rotation": 270}, "BACK": {"patternId": "P", "rotation": 180}, "LEFT": {"patternId": "arrow_down", "rotation": 180}, "RIGHT": {"patternId": "9", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C483\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> N -> N -> E -> E -> S -> E -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=P, rotation=180, flipVertical=true\n- step 2: patternId=arrow_down, rotation=270, flipVertical=true\n- step 3: patternId=star, rotation=90, flipVertical=true\n- step 4: patternId=9, rotation=90, flipVertical=true\n- step 5: patternId=P, rotation=0, flipVertical=true\n- step 6: patternId=arrow_down, rotation=90, flipVertical=true\n- step 7: patternId=star, rotation=270, flipVertical=true\n- step 8: patternId=F, rotation=180, flipVertical=true\n- step 9: patternId=9, rotation=0, flipVertical=true\n- step 10: patternId=P, rotation=270, flipVertical=true\n- allowed patternId values for this task: P, arrow_down, star, 9, F, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C483"} +{"sample_id": "C484", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> N -> E -> E -> N -> E -> W -> N -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "N", "E", "E", "N", "E", "W", "N", "S"], "observed_path_faces": [{"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C484_path_sequence.png"}, "metadata": {"level_id": 484, "name": "Reconstruct 484", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-484.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_up", "Q", "diamond", "R", "R", "square"], "start_x": 1, "start_y": 6, "grid_width": 6, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "arrow_up", "rotation": 270}, "BOTTOM": {"patternId": "square", "rotation": 270}, "FRONT": {"patternId": "Q", "rotation": 270}, "BACK": {"patternId": "R", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 90}, "RIGHT": {"patternId": "diamond", "rotation": 180}}, "bottom_faces": [{"patternId": "square", "rotation": 270, "x": 1, "y": 6}, {"patternId": "R", "rotation": 180, "x": 1, "y": 5}, {"patternId": "arrow_up", "rotation": 270, "x": 1, "y": 4}, {"patternId": "Q", "rotation": 270, "x": 1, "y": 3}, {"patternId": "diamond", "rotation": 180, "x": 2, "y": 3}, {"patternId": "R", "rotation": 0, "x": 3, "y": 3}, {"patternId": "square", "rotation": 90, "x": 3, "y": 2}, {"patternId": "R", "rotation": 180, "x": 4, "y": 2}, {"patternId": "square", "rotation": 90, "x": 3, "y": 2}, {"patternId": "Q", "rotation": 90, "x": 3, "y": 1}, {"patternId": "square", "rotation": 90, "x": 3, "y": 2}], "slot_sequence": ["BACK", "TOP", "FRONT", "RIGHT", "BACK", "BOTTOM", "LEFT", "BOTTOM", "FRONT", "BOTTOM"], "required_slots": ["BACK", "TOP", "FRONT", "RIGHT", "BOTTOM", "LEFT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "arrow_up", "rotation": 270}, "BOTTOM": {"patternId": "square", "rotation": 270}, "FRONT": {"patternId": "Q", "rotation": 270}, "BACK": {"patternId": "R", "rotation": 180}, "LEFT": {"patternId": "R", "rotation": 180}, "RIGHT": {"patternId": "diamond", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "arrow_up", "rotation": 270}, "BOTTOM": {"patternId": "square", "rotation": 270}, "FRONT": {"patternId": "Q", "rotation": 270}, "BACK": {"patternId": "R", "rotation": 180}, "LEFT": {"patternId": "R", "rotation": 180}, "RIGHT": {"patternId": "diamond", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C484\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> N -> E -> E -> N -> E -> W -> N -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=R, rotation=180, flipVertical=true\n- step 2: patternId=arrow_up, rotation=270, flipVertical=true\n- step 3: patternId=Q, rotation=270, flipVertical=true\n- step 4: patternId=diamond, rotation=180, flipVertical=true\n- step 5: patternId=R, rotation=0, flipVertical=true\n- step 6: patternId=square, rotation=90, flipVertical=true\n- step 7: patternId=R, rotation=180, flipVertical=true\n- step 8: patternId=square, rotation=90, flipVertical=true\n- step 9: patternId=Q, rotation=90, flipVertical=true\n- step 10: patternId=square, rotation=90, flipVertical=true\n- allowed patternId values for this task: R, arrow_up, Q, diamond, square, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C484"} +{"sample_id": "C485", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> E -> S -> W -> S -> W -> N -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "E", "S", "W", "S", "W", "N", "N", "N"], "observed_path_faces": [{"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C485_path_sequence.png"}, "metadata": {"level_id": 485, "name": "Reconstruct 485", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-485.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["B", "P", "D", "K", "heart", "arrow_left"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "B", "rotation": 180}, "BOTTOM": {"patternId": "arrow_left", "rotation": 270}, "FRONT": {"patternId": "P", "rotation": 90}, "BACK": {"patternId": "K", "rotation": 90}, "LEFT": {"patternId": "heart", "rotation": 270}, "RIGHT": {"patternId": "D", "rotation": 180}}, "bottom_faces": [{"patternId": "arrow_left", "rotation": 270, "x": 1, "y": 1}, {"patternId": "P", "rotation": 90, "x": 1, "y": 2}, {"patternId": "D", "rotation": 180, "x": 2, "y": 2}, {"patternId": "K", "rotation": 90, "x": 3, "y": 2}, {"patternId": "B", "rotation": 0, "x": 3, "y": 3}, {"patternId": "D", "rotation": 270, "x": 2, "y": 3}, {"patternId": "P", "rotation": 180, "x": 2, "y": 4}, {"patternId": "arrow_left", "rotation": 0, "x": 1, "y": 4}, {"patternId": "D", "rotation": 0, "x": 1, "y": 3}, {"patternId": "B", "rotation": 90, "x": 1, "y": 2}, {"patternId": "heart", "rotation": 270, "x": 1, "y": 1}], "slot_sequence": ["FRONT", "RIGHT", "BACK", "TOP", "RIGHT", "FRONT", "BOTTOM", "RIGHT", "TOP", "LEFT"], "required_slots": ["FRONT", "RIGHT", "BACK", "TOP", "BOTTOM", "LEFT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "B", "rotation": 180}, "BOTTOM": {"patternId": "arrow_left", "rotation": 270}, "FRONT": {"patternId": "P", "rotation": 90}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "heart", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "B", "rotation": 180}, "BOTTOM": {"patternId": "arrow_left", "rotation": 270}, "FRONT": {"patternId": "P", "rotation": 90}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "heart", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C485\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> E -> S -> W -> S -> W -> N -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=P, rotation=90, flipVertical=true\n- step 2: patternId=D, rotation=180, flipVertical=true\n- step 3: patternId=K, rotation=90, flipVertical=true\n- step 4: patternId=B, rotation=0, flipVertical=true\n- step 5: patternId=D, rotation=270, flipVertical=true\n- step 6: patternId=P, rotation=180, flipVertical=true\n- step 7: patternId=arrow_left, rotation=0, flipVertical=true\n- step 8: patternId=D, rotation=0, flipVertical=true\n- step 9: patternId=B, rotation=90, flipVertical=true\n- step 10: patternId=heart, rotation=270, flipVertical=true\n- allowed patternId values for this task: P, D, K, B, arrow_left, heart, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C485"} +{"sample_id": "C486", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> S -> E -> W -> S -> W -> N -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "W", "S", "E", "W", "S", "W", "N", "W", "W"], "observed_path_faces": [{"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C486_path_sequence.png"}, "metadata": {"level_id": 486, "name": "Reconstruct 486", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-486.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["circle", "H", "W", "2", "K", "arrow_left"], "start_x": 5, "start_y": 1, "grid_width": 7, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "circle", "rotation": 270}, "BOTTOM": {"patternId": "arrow_left", "rotation": 270}, "FRONT": {"patternId": "H", "rotation": 270}, "BACK": {"patternId": "2", "rotation": 90}, "LEFT": {"patternId": "K", "rotation": 180}, "RIGHT": {"patternId": "W", "rotation": 0}}, "bottom_faces": [{"patternId": "arrow_left", "rotation": 270, "x": 5, "y": 1}, {"patternId": "H", "rotation": 270, "x": 5, "y": 2}, {"patternId": "K", "rotation": 180, "x": 4, "y": 2}, {"patternId": "circle", "rotation": 180, "x": 4, "y": 3}, {"patternId": "H", "rotation": 180, "x": 5, "y": 3}, {"patternId": "circle", "rotation": 180, "x": 4, "y": 3}, {"patternId": "W", "rotation": 180, "x": 4, "y": 4}, {"patternId": "2", "rotation": 270, "x": 3, "y": 4}, {"patternId": "circle", "rotation": 270, "x": 3, "y": 3}, {"patternId": "K", "rotation": 270, "x": 2, "y": 3}, {"patternId": "arrow_left", "rotation": 90, "x": 1, "y": 3}], "slot_sequence": ["FRONT", "LEFT", "TOP", "FRONT", "TOP", "RIGHT", "BACK", "TOP", "LEFT", "BOTTOM"], "required_slots": ["FRONT", "LEFT", "TOP", "RIGHT", "BACK", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "circle", "rotation": 270}, "BOTTOM": {"patternId": "arrow_left", "rotation": 270}, "FRONT": {"patternId": "H", "rotation": 270}, "BACK": {"patternId": "2", "rotation": 270}, "LEFT": {"patternId": "K", "rotation": 270}, "RIGHT": {"patternId": "W", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 270}, "BOTTOM": {"patternId": "arrow_left", "rotation": 270}, "FRONT": {"patternId": "H", "rotation": 270}, "BACK": {"patternId": "2", "rotation": 270}, "LEFT": {"patternId": "K", "rotation": 270}, "RIGHT": {"patternId": "W", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C486\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> S -> E -> W -> S -> W -> N -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=H, rotation=270, flipVertical=true\n- step 2: patternId=K, rotation=180, flipVertical=true\n- step 3: patternId=circle, rotation=180, flipVertical=true\n- step 4: patternId=H, rotation=180, flipVertical=true\n- step 5: patternId=circle, rotation=180, flipVertical=true\n- step 6: patternId=W, rotation=180, flipVertical=true\n- step 7: patternId=2, rotation=270, flipVertical=true\n- step 8: patternId=circle, rotation=270, flipVertical=true\n- step 9: patternId=K, rotation=270, flipVertical=true\n- step 10: patternId=arrow_left, rotation=90, flipVertical=true\n- allowed patternId values for this task: H, K, circle, W, 2, arrow_left, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C486"} +{"sample_id": "C487", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> S -> E -> N -> N -> N -> S -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "S", "E", "N", "N", "N", "S", "N", "N"], "observed_path_faces": [{"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C487_path_sequence.png"}, "metadata": {"level_id": 487, "name": "Reconstruct 487", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-487.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_right", "E", "D", "arrow_up", "D", "6"], "start_x": 1, "start_y": 3, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "arrow_right", "rotation": 90}, "BOTTOM": {"patternId": "6", "rotation": 270}, "FRONT": {"patternId": "E", "rotation": 90}, "BACK": {"patternId": "arrow_up", "rotation": 180}, "LEFT": {"patternId": "D", "rotation": 270}, "RIGHT": {"patternId": "D", "rotation": 270}}, "bottom_faces": [{"patternId": "6", "rotation": 270, "x": 1, "y": 3}, {"patternId": "E", "rotation": 90, "x": 1, "y": 4}, {"patternId": "D", "rotation": 270, "x": 2, "y": 4}, {"patternId": "arrow_right", "rotation": 180, "x": 2, "y": 5}, {"patternId": "arrow_up", "rotation": 90, "x": 3, "y": 5}, {"patternId": "D", "rotation": 180, "x": 3, "y": 4}, {"patternId": "E", "rotation": 0, "x": 3, "y": 3}, {"patternId": "D", "rotation": 180, "x": 3, "y": 2}, {"patternId": "E", "rotation": 0, "x": 3, "y": 3}, {"patternId": "D", "rotation": 180, "x": 3, "y": 2}, {"patternId": "arrow_up", "rotation": 90, "x": 3, "y": 1}], "slot_sequence": ["FRONT", "RIGHT", "TOP", "BACK", "RIGHT", "FRONT", "LEFT", "FRONT", "LEFT", "BACK"], "required_slots": ["FRONT", "RIGHT", "TOP", "BACK", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "arrow_right", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "E", "rotation": 90}, "BACK": {"patternId": "arrow_up", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "arrow_right", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "E", "rotation": 90}, "BACK": {"patternId": "arrow_up", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C487\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> S -> E -> N -> N -> N -> S -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=E, rotation=90, flipVertical=true\n- step 2: patternId=D, rotation=270, flipVertical=true\n- step 3: patternId=arrow_right, rotation=180, flipVertical=true\n- step 4: patternId=arrow_up, rotation=90, flipVertical=true\n- step 5: patternId=D, rotation=180, flipVertical=true\n- step 6: patternId=E, rotation=0, flipVertical=true\n- step 7: patternId=D, rotation=180, flipVertical=true\n- step 8: patternId=E, rotation=0, flipVertical=true\n- step 9: patternId=D, rotation=180, flipVertical=true\n- step 10: patternId=arrow_up, rotation=90, flipVertical=true\n- allowed patternId values for this task: E, D, arrow_right, arrow_up, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C487"} +{"sample_id": "C488", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> S -> S -> S -> E -> S -> E -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "S", "S", "S", "E", "S", "E", "N", "N"], "observed_path_faces": [{"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C488_path_sequence.png"}, "metadata": {"level_id": 488, "name": "Reconstruct 488", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-488.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Y", "arrow_down", "M", "M", "Q", "X"], "start_x": 2, "start_y": 2, "grid_width": 5, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "Y", "rotation": 0}, "BOTTOM": {"patternId": "X", "rotation": 0}, "FRONT": {"patternId": "arrow_down", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 180}, "LEFT": {"patternId": "Q", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 270}}, "bottom_faces": [{"patternId": "X", "rotation": 0, "x": 2, "y": 2}, {"patternId": "M", "rotation": 0, "x": 2, "y": 1}, {"patternId": "Q", "rotation": 180, "x": 1, "y": 1}, {"patternId": "X", "rotation": 270, "x": 1, "y": 2}, {"patternId": "M", "rotation": 270, "x": 1, "y": 3}, {"patternId": "Y", "rotation": 90, "x": 1, "y": 4}, {"patternId": "M", "rotation": 90, "x": 2, "y": 4}, {"patternId": "Q", "rotation": 270, "x": 2, "y": 5}, {"patternId": "X", "rotation": 0, "x": 3, "y": 5}, {"patternId": "M", "rotation": 0, "x": 3, "y": 4}, {"patternId": "Y", "rotation": 0, "x": 3, "y": 3}], "slot_sequence": ["BACK", "LEFT", "BOTTOM", "RIGHT", "TOP", "BACK", "LEFT", "BOTTOM", "BACK", "TOP"], "required_slots": ["BACK", "LEFT", "BOTTOM", "RIGHT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "Y", "rotation": 0}, "BOTTOM": {"patternId": "X", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "Q", "rotation": 90}, "RIGHT": {"patternId": "M", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "Y", "rotation": 0}, "BOTTOM": {"patternId": "X", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "Q", "rotation": 90}, "RIGHT": {"patternId": "M", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C488\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> S -> S -> S -> E -> S -> E -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=M, rotation=0, flipVertical=true\n- step 2: patternId=Q, rotation=180, flipVertical=true\n- step 3: patternId=X, rotation=270, flipVertical=true\n- step 4: patternId=M, rotation=270, flipVertical=true\n- step 5: patternId=Y, rotation=90, flipVertical=true\n- step 6: patternId=M, rotation=90, flipVertical=true\n- step 7: patternId=Q, rotation=270, flipVertical=true\n- step 8: patternId=X, rotation=0, flipVertical=true\n- step 9: patternId=M, rotation=0, flipVertical=true\n- step 10: patternId=Y, rotation=0, flipVertical=true\n- allowed patternId values for this task: M, Q, X, Y, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C488"} +{"sample_id": "C489", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> E -> S -> E -> N -> W -> W -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "E", "S", "E", "N", "W", "W", "S", "S"], "observed_path_faces": [{"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C489_path_sequence.png"}, "metadata": {"level_id": 489, "name": "Reconstruct 489", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-489.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["smile", "diamond", "M", "diamond", "X", "6"], "start_x": 1, "start_y": 3, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "smile", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 270}, "FRONT": {"patternId": "diamond", "rotation": 270}, "BACK": {"patternId": "diamond", "rotation": 180}, "LEFT": {"patternId": "X", "rotation": 270}, "RIGHT": {"patternId": "M", "rotation": 180}}, "bottom_faces": [{"patternId": "6", "rotation": 270, "x": 1, "y": 3}, {"patternId": "diamond", "rotation": 0, "x": 1, "y": 2}, {"patternId": "smile", "rotation": 0, "x": 1, "y": 1}, {"patternId": "M", "rotation": 90, "x": 2, "y": 1}, {"patternId": "diamond", "rotation": 90, "x": 2, "y": 2}, {"patternId": "6", "rotation": 0, "x": 3, "y": 2}, {"patternId": "M", "rotation": 0, "x": 3, "y": 1}, {"patternId": "diamond", "rotation": 0, "x": 2, "y": 1}, {"patternId": "X", "rotation": 90, "x": 1, "y": 1}, {"patternId": "6", "rotation": 180, "x": 1, "y": 2}, {"patternId": "M", "rotation": 180, "x": 1, "y": 3}], "slot_sequence": ["BACK", "TOP", "RIGHT", "BACK", "BOTTOM", "RIGHT", "BACK", "LEFT", "BOTTOM", "RIGHT"], "required_slots": ["BACK", "TOP", "RIGHT", "BOTTOM", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "smile", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "diamond", "rotation": 0}, "LEFT": {"patternId": "X", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "diamond", "rotation": 0}, "LEFT": {"patternId": "X", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C489\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> E -> S -> E -> N -> W -> W -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=diamond, rotation=0, flipVertical=true\n- step 2: patternId=smile, rotation=0, flipVertical=true\n- step 3: patternId=M, rotation=90, flipVertical=true\n- step 4: patternId=diamond, rotation=90, flipVertical=true\n- step 5: patternId=6, rotation=0, flipVertical=true\n- step 6: patternId=M, rotation=0, flipVertical=true\n- step 7: patternId=diamond, rotation=0, flipVertical=true\n- step 8: patternId=X, rotation=90, flipVertical=true\n- step 9: patternId=6, rotation=180, flipVertical=true\n- step 10: patternId=M, rotation=180, flipVertical=true\n- allowed patternId values for this task: diamond, smile, M, 6, X, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C489"} +{"sample_id": "C490", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> W -> S -> W -> N -> W -> N -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "W", "S", "W", "N", "W", "N", "W", "S"], "observed_path_faces": [{"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C490_path_sequence.png"}, "metadata": {"level_id": 490, "name": "Reconstruct 490", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-490.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["2", "E", "S", "Z", "N", "5"], "start_x": 4, "start_y": 3, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "2", "rotation": 270}, "BOTTOM": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "E", "rotation": 0}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "N", "rotation": 90}, "RIGHT": {"patternId": "S", "rotation": 180}}, "bottom_faces": [{"patternId": "5", "rotation": 90, "x": 4, "y": 3}, {"patternId": "Z", "rotation": 90, "x": 4, "y": 2}, {"patternId": "S", "rotation": 0, "x": 5, "y": 2}, {"patternId": "Z", "rotation": 90, "x": 4, "y": 2}, {"patternId": "5", "rotation": 90, "x": 4, "y": 3}, {"patternId": "N", "rotation": 0, "x": 3, "y": 3}, {"patternId": "Z", "rotation": 180, "x": 3, "y": 2}, {"patternId": "2", "rotation": 0, "x": 2, "y": 2}, {"patternId": "S", "rotation": 180, "x": 2, "y": 1}, {"patternId": "E", "rotation": 0, "x": 1, "y": 1}, {"patternId": "2", "rotation": 270, "x": 1, "y": 2}], "slot_sequence": ["BACK", "RIGHT", "BACK", "BOTTOM", "LEFT", "BACK", "TOP", "RIGHT", "FRONT", "TOP"], "required_slots": ["BACK", "RIGHT", "BOTTOM", "LEFT", "TOP", "FRONT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "2", "rotation": 270}, "BOTTOM": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "E", "rotation": 0}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "N", "rotation": 180}, "RIGHT": {"patternId": "S", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "2", "rotation": 270}, "BOTTOM": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "E", "rotation": 0}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "N", "rotation": 180}, "RIGHT": {"patternId": "S", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C490\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> W -> S -> W -> N -> W -> N -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Z, rotation=90, flipVertical=true\n- step 2: patternId=S, rotation=0, flipVertical=true\n- step 3: patternId=Z, rotation=90, flipVertical=true\n- step 4: patternId=5, rotation=90, flipVertical=true\n- step 5: patternId=N, rotation=0, flipVertical=true\n- step 6: patternId=Z, rotation=180, flipVertical=true\n- step 7: patternId=2, rotation=0, flipVertical=true\n- step 8: patternId=S, rotation=180, flipVertical=true\n- step 9: patternId=E, rotation=0, flipVertical=true\n- step 10: patternId=2, rotation=270, flipVertical=true\n- allowed patternId values for this task: Z, S, 5, N, 2, E, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C490"} +{"sample_id": "C491", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> W -> W -> N -> W -> N -> E -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "W", "W", "N", "W", "N", "E", "E", "S"], "observed_path_faces": [{"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C491_path_sequence.png"}, "metadata": {"level_id": 491, "name": "Reconstruct 491", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-491.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["4", "U", "X", "B", "Z", "arrow_left"], "start_x": 2, "start_y": 3, "grid_width": 6, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "4", "rotation": 270}, "BOTTOM": {"patternId": "arrow_left", "rotation": 180}, "FRONT": {"patternId": "U", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 180}, "LEFT": {"patternId": "Z", "rotation": 180}, "RIGHT": {"patternId": "X", "rotation": 90}}, "bottom_faces": [{"patternId": "arrow_left", "rotation": 180, "x": 2, "y": 3}, {"patternId": "X", "rotation": 180, "x": 3, "y": 3}, {"patternId": "4", "rotation": 90, "x": 4, "y": 3}, {"patternId": "X", "rotation": 180, "x": 3, "y": 3}, {"patternId": "arrow_left", "rotation": 180, "x": 2, "y": 3}, {"patternId": "B", "rotation": 0, "x": 2, "y": 2}, {"patternId": "Z", "rotation": 0, "x": 1, "y": 2}, {"patternId": "4", "rotation": 0, "x": 1, "y": 1}, {"patternId": "B", "rotation": 90, "x": 2, "y": 1}, {"patternId": "arrow_left", "rotation": 270, "x": 3, "y": 1}, {"patternId": "Z", "rotation": 180, "x": 3, "y": 2}], "slot_sequence": ["RIGHT", "TOP", "RIGHT", "BOTTOM", "BACK", "LEFT", "TOP", "BACK", "BOTTOM", "LEFT"], "required_slots": ["RIGHT", "TOP", "BOTTOM", "BACK", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "4", "rotation": 270}, "BOTTOM": {"patternId": "arrow_left", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "Z", "rotation": 270}, "RIGHT": {"patternId": "X", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "4", "rotation": 270}, "BOTTOM": {"patternId": "arrow_left", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "Z", "rotation": 270}, "RIGHT": {"patternId": "X", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C491\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> W -> W -> N -> W -> N -> E -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=X, rotation=180, flipVertical=true\n- step 2: patternId=4, rotation=90, flipVertical=true\n- step 3: patternId=X, rotation=180, flipVertical=true\n- step 4: patternId=arrow_left, rotation=180, flipVertical=true\n- step 5: patternId=B, rotation=0, flipVertical=true\n- step 6: patternId=Z, rotation=0, flipVertical=true\n- step 7: patternId=4, rotation=0, flipVertical=true\n- step 8: patternId=B, rotation=90, flipVertical=true\n- step 9: patternId=arrow_left, rotation=270, flipVertical=true\n- step 10: patternId=Z, rotation=180, flipVertical=true\n- allowed patternId values for this task: X, 4, arrow_left, B, Z, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C491"} +{"sample_id": "C492", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> N -> N -> E -> E -> S -> E -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "W", "N", "N", "E", "E", "S", "E", "N", "N"], "observed_path_faces": [{"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C492_path_sequence.png"}, "metadata": {"level_id": 492, "name": "Reconstruct 492", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-492.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["K", "star", "X", "F", "F", "S"], "start_x": 2, "start_y": 5, "grid_width": 6, "grid_height": 7, "true_solution_faces": {"TOP": {"patternId": "K", "rotation": 270}, "BOTTOM": {"patternId": "S", "rotation": 270}, "FRONT": {"patternId": "star", "rotation": 270}, "BACK": {"patternId": "F", "rotation": 180}, "LEFT": {"patternId": "F", "rotation": 90}, "RIGHT": {"patternId": "X", "rotation": 0}}, "bottom_faces": [{"patternId": "S", "rotation": 270, "x": 2, "y": 5}, {"patternId": "F", "rotation": 0, "x": 2, "y": 4}, {"patternId": "F", "rotation": 270, "x": 1, "y": 4}, {"patternId": "K", "rotation": 0, "x": 1, "y": 3}, {"patternId": "X", "rotation": 0, "x": 1, "y": 2}, {"patternId": "F", "rotation": 180, "x": 2, "y": 2}, {"patternId": "F", "rotation": 90, "x": 3, "y": 2}, {"patternId": "K", "rotation": 180, "x": 3, "y": 3}, {"patternId": "star", "rotation": 180, "x": 4, "y": 3}, {"patternId": "F", "rotation": 0, "x": 4, "y": 2}, {"patternId": "F", "rotation": 90, "x": 4, "y": 1}], "slot_sequence": ["BACK", "LEFT", "TOP", "RIGHT", "BACK", "LEFT", "TOP", "FRONT", "LEFT", "BACK"], "required_slots": ["BACK", "LEFT", "TOP", "RIGHT", "FRONT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "K", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 270}, "BACK": {"patternId": "F", "rotation": 0}, "LEFT": {"patternId": "F", "rotation": 180}, "RIGHT": {"patternId": "X", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "K", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 270}, "BACK": {"patternId": "F", "rotation": 0}, "LEFT": {"patternId": "F", "rotation": 180}, "RIGHT": {"patternId": "X", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C492\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> N -> N -> E -> E -> S -> E -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=F, rotation=0, flipVertical=true\n- step 2: patternId=F, rotation=270, flipVertical=true\n- step 3: patternId=K, rotation=0, flipVertical=true\n- step 4: patternId=X, rotation=0, flipVertical=true\n- step 5: patternId=F, rotation=180, flipVertical=true\n- step 6: patternId=F, rotation=90, flipVertical=true\n- step 7: patternId=K, rotation=180, flipVertical=true\n- step 8: patternId=star, rotation=180, flipVertical=true\n- step 9: patternId=F, rotation=0, flipVertical=true\n- step 10: patternId=F, rotation=90, flipVertical=true\n- allowed patternId values for this task: F, K, X, star, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C492"} +{"sample_id": "C493", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> N -> N -> S -> E -> S -> W -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "N", "N", "N", "S", "E", "S", "W", "W", "N"], "observed_path_faces": [{"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C493_path_sequence.png"}, "metadata": {"level_id": 493, "name": "Reconstruct 493", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-493.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["5", "B", "arrow_up", "W", "star", "X"], "start_x": 1, "start_y": 4, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "X", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 270}, "BACK": {"patternId": "W", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 0}, "RIGHT": {"patternId": "arrow_up", "rotation": 90}}, "bottom_faces": [{"patternId": "X", "rotation": 0, "x": 1, "y": 4}, {"patternId": "arrow_up", "rotation": 180, "x": 2, "y": 4}, {"patternId": "W", "rotation": 90, "x": 2, "y": 3}, {"patternId": "star", "rotation": 90, "x": 2, "y": 2}, {"patternId": "B", "rotation": 0, "x": 2, "y": 1}, {"patternId": "star", "rotation": 90, "x": 2, "y": 2}, {"patternId": "5", "rotation": 90, "x": 3, "y": 2}, {"patternId": "W", "rotation": 180, "x": 3, "y": 3}, {"patternId": "star", "rotation": 180, "x": 2, "y": 3}, {"patternId": "B", "rotation": 90, "x": 1, "y": 3}, {"patternId": "5", "rotation": 270, "x": 1, "y": 2}], "slot_sequence": ["RIGHT", "BACK", "LEFT", "FRONT", "LEFT", "TOP", "BACK", "LEFT", "FRONT", "TOP"], "required_slots": ["RIGHT", "BACK", "LEFT", "FRONT", "TOP"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 270}, "BACK": {"patternId": "W", "rotation": 180}, "LEFT": {"patternId": "star", "rotation": 90}, "RIGHT": {"patternId": "arrow_up", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 270}, "BACK": {"patternId": "W", "rotation": 180}, "LEFT": {"patternId": "star", "rotation": 90}, "RIGHT": {"patternId": "arrow_up", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C493\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> N -> N -> S -> E -> S -> W -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_up, rotation=180, flipVertical=true\n- step 2: patternId=W, rotation=90, flipVertical=true\n- step 3: patternId=star, rotation=90, flipVertical=true\n- step 4: patternId=B, rotation=0, flipVertical=true\n- step 5: patternId=star, rotation=90, flipVertical=true\n- step 6: patternId=5, rotation=90, flipVertical=true\n- step 7: patternId=W, rotation=180, flipVertical=true\n- step 8: patternId=star, rotation=180, flipVertical=true\n- step 9: patternId=B, rotation=90, flipVertical=true\n- step 10: patternId=5, rotation=270, flipVertical=true\n- allowed patternId values for this task: arrow_up, W, star, B, 5, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C493"} +{"sample_id": "C494", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> S -> N -> N -> E -> S -> E -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "S", "S", "N", "N", "E", "S", "E", "W", "N"], "observed_path_faces": [{"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C494_path_sequence.png"}, "metadata": {"level_id": 494, "name": "Reconstruct 494", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-494.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["C", "S", "plus", "W", "T", "smile"], "start_x": 2, "start_y": 1, "grid_width": 5, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "C", "rotation": 0}, "BOTTOM": {"patternId": "smile", "rotation": 180}, "FRONT": {"patternId": "S", "rotation": 180}, "BACK": {"patternId": "W", "rotation": 90}, "LEFT": {"patternId": "T", "rotation": 270}, "RIGHT": {"patternId": "plus", "rotation": 0}}, "bottom_faces": [{"patternId": "smile", "rotation": 180, "x": 2, "y": 1}, {"patternId": "T", "rotation": 180, "x": 1, "y": 1}, {"patternId": "S", "rotation": 90, "x": 1, "y": 2}, {"patternId": "plus", "rotation": 270, "x": 1, "y": 3}, {"patternId": "S", "rotation": 90, "x": 1, "y": 2}, {"patternId": "T", "rotation": 180, "x": 1, "y": 1}, {"patternId": "smile", "rotation": 180, "x": 2, "y": 1}, {"patternId": "S", "rotation": 180, "x": 2, "y": 2}, {"patternId": "plus", "rotation": 0, "x": 3, "y": 2}, {"patternId": "S", "rotation": 180, "x": 2, "y": 2}, {"patternId": "smile", "rotation": 180, "x": 2, "y": 1}], "slot_sequence": ["LEFT", "FRONT", "RIGHT", "FRONT", "LEFT", "BOTTOM", "FRONT", "RIGHT", "FRONT", "BOTTOM"], "required_slots": ["LEFT", "FRONT", "RIGHT", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "smile", "rotation": 180}, "FRONT": {"patternId": "S", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "T", "rotation": 0}, "RIGHT": {"patternId": "plus", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "smile", "rotation": 180}, "FRONT": {"patternId": "S", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "T", "rotation": 0}, "RIGHT": {"patternId": "plus", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C494\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> S -> N -> N -> E -> S -> E -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=T, rotation=180, flipVertical=true\n- step 2: patternId=S, rotation=90, flipVertical=true\n- step 3: patternId=plus, rotation=270, flipVertical=true\n- step 4: patternId=S, rotation=90, flipVertical=true\n- step 5: patternId=T, rotation=180, flipVertical=true\n- step 6: patternId=smile, rotation=180, flipVertical=true\n- step 7: patternId=S, rotation=180, flipVertical=true\n- step 8: patternId=plus, rotation=0, flipVertical=true\n- step 9: patternId=S, rotation=180, flipVertical=true\n- step 10: patternId=smile, rotation=180, flipVertical=true\n- allowed patternId values for this task: T, S, plus, smile, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C494"} +{"sample_id": "C495", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> S -> W -> S -> S -> N -> W -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "N", "S", "W", "S", "S", "N", "W", "N", "W"], "observed_path_faces": [{"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C495_path_sequence.png"}, "metadata": {"level_id": 495, "name": "Reconstruct 495", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-495.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["K", "S", "heart", "X", "circle", "R"], "start_x": 4, "start_y": 3, "grid_width": 6, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "K", "rotation": 270}, "BOTTOM": {"patternId": "R", "rotation": 270}, "FRONT": {"patternId": "S", "rotation": 90}, "BACK": {"patternId": "X", "rotation": 180}, "LEFT": {"patternId": "circle", "rotation": 270}, "RIGHT": {"patternId": "heart", "rotation": 270}}, "bottom_faces": [{"patternId": "R", "rotation": 270, "x": 4, "y": 3}, {"patternId": "X", "rotation": 0, "x": 4, "y": 2}, {"patternId": "K", "rotation": 270, "x": 4, "y": 1}, {"patternId": "X", "rotation": 0, "x": 4, "y": 2}, {"patternId": "circle", "rotation": 90, "x": 3, "y": 2}, {"patternId": "R", "rotation": 180, "x": 3, "y": 3}, {"patternId": "heart", "rotation": 270, "x": 3, "y": 4}, {"patternId": "R", "rotation": 180, "x": 3, "y": 3}, {"patternId": "S", "rotation": 0, "x": 2, "y": 3}, {"patternId": "circle", "rotation": 180, "x": 2, "y": 2}, {"patternId": "K", "rotation": 90, "x": 1, "y": 2}], "slot_sequence": ["BACK", "TOP", "BACK", "LEFT", "BOTTOM", "RIGHT", "BOTTOM", "FRONT", "LEFT", "TOP"], "required_slots": ["BACK", "TOP", "LEFT", "BOTTOM", "RIGHT", "FRONT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "K", "rotation": 270}, "BOTTOM": {"patternId": "R", "rotation": 270}, "FRONT": {"patternId": "S", "rotation": 90}, "BACK": {"patternId": "X", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 0}, "RIGHT": {"patternId": "heart", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "K", "rotation": 270}, "BOTTOM": {"patternId": "R", "rotation": 270}, "FRONT": {"patternId": "S", "rotation": 90}, "BACK": {"patternId": "X", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 0}, "RIGHT": {"patternId": "heart", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C495\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> S -> W -> S -> S -> N -> W -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=X, rotation=0, flipVertical=true\n- step 2: patternId=K, rotation=270, flipVertical=true\n- step 3: patternId=X, rotation=0, flipVertical=true\n- step 4: patternId=circle, rotation=90, flipVertical=true\n- step 5: patternId=R, rotation=180, flipVertical=true\n- step 6: patternId=heart, rotation=270, flipVertical=true\n- step 7: patternId=R, rotation=180, flipVertical=true\n- step 8: patternId=S, rotation=0, flipVertical=true\n- step 9: patternId=circle, rotation=180, flipVertical=true\n- step 10: patternId=K, rotation=90, flipVertical=true\n- allowed patternId values for this task: X, K, circle, R, heart, S, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C495"} +{"sample_id": "C496", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> S -> N -> N -> E -> N -> E -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "S", "N", "N", "E", "N", "E", "N", "N"], "observed_path_faces": [{"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C496_path_sequence.png"}, "metadata": {"level_id": 496, "name": "Reconstruct 496", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-496.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["Z", "6", "Z", "2", "1", "G"], "start_x": 1, "start_y": 4, "grid_width": 6, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "Z", "rotation": 0}, "BOTTOM": {"patternId": "G", "rotation": 270}, "FRONT": {"patternId": "6", "rotation": 180}, "BACK": {"patternId": "2", "rotation": 270}, "LEFT": {"patternId": "1", "rotation": 270}, "RIGHT": {"patternId": "Z", "rotation": 90}}, "bottom_faces": [{"patternId": "G", "rotation": 270, "x": 1, "y": 4}, {"patternId": "Z", "rotation": 180, "x": 2, "y": 4}, {"patternId": "6", "rotation": 270, "x": 2, "y": 5}, {"patternId": "1", "rotation": 0, "x": 2, "y": 6}, {"patternId": "6", "rotation": 270, "x": 2, "y": 5}, {"patternId": "Z", "rotation": 180, "x": 2, "y": 4}, {"patternId": "Z", "rotation": 180, "x": 3, "y": 4}, {"patternId": "2", "rotation": 270, "x": 3, "y": 3}, {"patternId": "1", "rotation": 270, "x": 4, "y": 3}, {"patternId": "G", "rotation": 0, "x": 4, "y": 2}, {"patternId": "Z", "rotation": 270, "x": 4, "y": 1}], "slot_sequence": ["RIGHT", "FRONT", "LEFT", "FRONT", "RIGHT", "TOP", "BACK", "LEFT", "BOTTOM", "RIGHT"], "required_slots": ["RIGHT", "FRONT", "LEFT", "TOP", "BACK", "BOTTOM"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "Z", "rotation": 0}, "BOTTOM": {"patternId": "G", "rotation": 270}, "FRONT": {"patternId": "6", "rotation": 180}, "BACK": {"patternId": "2", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "Z", "rotation": 0}, "BOTTOM": {"patternId": "G", "rotation": 270}, "FRONT": {"patternId": "6", "rotation": 180}, "BACK": {"patternId": "2", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C496\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> S -> N -> N -> E -> N -> E -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Z, rotation=180, flipVertical=true\n- step 2: patternId=6, rotation=270, flipVertical=true\n- step 3: patternId=1, rotation=0, flipVertical=true\n- step 4: patternId=6, rotation=270, flipVertical=true\n- step 5: patternId=Z, rotation=180, flipVertical=true\n- step 6: patternId=Z, rotation=180, flipVertical=true\n- step 7: patternId=2, rotation=270, flipVertical=true\n- step 8: patternId=1, rotation=270, flipVertical=true\n- step 9: patternId=G, rotation=0, flipVertical=true\n- step 10: patternId=Z, rotation=270, flipVertical=true\n- allowed patternId values for this task: Z, 6, 1, 2, G, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C496"} +{"sample_id": "C497", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> N -> N -> W -> S -> W -> S -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["S", "E", "N", "N", "W", "S", "W", "S", "W", "W"], "observed_path_faces": [{"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C497_path_sequence.png"}, "metadata": {"level_id": 497, "name": "Reconstruct 497", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-497.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["3", "Z", "2", "F", "4", "2"], "start_x": 4, "start_y": 2, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "3", "rotation": 270}, "BOTTOM": {"patternId": "2", "rotation": 0}, "FRONT": {"patternId": "Z", "rotation": 0}, "BACK": {"patternId": "F", "rotation": 0}, "LEFT": {"patternId": "4", "rotation": 180}, "RIGHT": {"patternId": "2", "rotation": 180}}, "bottom_faces": [{"patternId": "2", "rotation": 0, "x": 4, "y": 2}, {"patternId": "Z", "rotation": 0, "x": 4, "y": 3}, {"patternId": "2", "rotation": 180, "x": 5, "y": 3}, {"patternId": "2", "rotation": 270, "x": 5, "y": 2}, {"patternId": "4", "rotation": 0, "x": 5, "y": 1}, {"patternId": "Z", "rotation": 180, "x": 4, "y": 1}, {"patternId": "2", "rotation": 180, "x": 4, "y": 2}, {"patternId": "2", "rotation": 90, "x": 3, "y": 2}, {"patternId": "F", "rotation": 270, "x": 3, "y": 3}, {"patternId": "3", "rotation": 0, "x": 2, "y": 3}, {"patternId": "Z", "rotation": 90, "x": 1, "y": 3}], "slot_sequence": ["FRONT", "RIGHT", "BOTTOM", "LEFT", "FRONT", "BOTTOM", "RIGHT", "BACK", "TOP", "FRONT"], "required_slots": ["FRONT", "RIGHT", "BOTTOM", "LEFT", "BACK", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "3", "rotation": 270}, "BOTTOM": {"patternId": "2", "rotation": 0}, "FRONT": {"patternId": "Z", "rotation": 0}, "BACK": {"patternId": "F", "rotation": 180}, "LEFT": {"patternId": "4", "rotation": 270}, "RIGHT": {"patternId": "2", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "3", "rotation": 270}, "BOTTOM": {"patternId": "2", "rotation": 0}, "FRONT": {"patternId": "Z", "rotation": 0}, "BACK": {"patternId": "F", "rotation": 180}, "LEFT": {"patternId": "4", "rotation": 270}, "RIGHT": {"patternId": "2", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C497\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> N -> N -> W -> S -> W -> S -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Z, rotation=0, flipVertical=true\n- step 2: patternId=2, rotation=180, flipVertical=true\n- step 3: patternId=2, rotation=270, flipVertical=true\n- step 4: patternId=4, rotation=0, flipVertical=true\n- step 5: patternId=Z, rotation=180, flipVertical=true\n- step 6: patternId=2, rotation=180, flipVertical=true\n- step 7: patternId=2, rotation=90, flipVertical=true\n- step 8: patternId=F, rotation=270, flipVertical=true\n- step 9: patternId=3, rotation=0, flipVertical=true\n- step 10: patternId=Z, rotation=90, flipVertical=true\n- allowed patternId values for this task: Z, 2, 4, F, 3, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C497"} +{"sample_id": "C498", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> S -> S -> W -> E -> E -> S -> S -> N\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "S", "S", "W", "E", "E", "S", "S", "N"], "observed_path_faces": [{"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C498_path_sequence.png"}, "metadata": {"level_id": 498, "name": "Reconstruct 498", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-498.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["arrow_left", "J", "circle", "heart", "triangle", "arrow_up"], "start_x": 1, "start_y": 1, "grid_width": 5, "grid_height": 8, "true_solution_faces": {"TOP": {"patternId": "arrow_left", "rotation": 90}, "BOTTOM": {"patternId": "arrow_up", "rotation": 90}, "FRONT": {"patternId": "J", "rotation": 270}, "BACK": {"patternId": "heart", "rotation": 0}, "LEFT": {"patternId": "triangle", "rotation": 0}, "RIGHT": {"patternId": "circle", "rotation": 90}}, "bottom_faces": [{"patternId": "arrow_up", "rotation": 90, "x": 1, "y": 1}, {"patternId": "circle", "rotation": 180, "x": 2, "y": 1}, {"patternId": "J", "rotation": 0, "x": 2, "y": 2}, {"patternId": "triangle", "rotation": 90, "x": 2, "y": 3}, {"patternId": "heart", "rotation": 90, "x": 2, "y": 4}, {"patternId": "arrow_up", "rotation": 0, "x": 1, "y": 4}, {"patternId": "heart", "rotation": 90, "x": 2, "y": 4}, {"patternId": "arrow_left", "rotation": 0, "x": 3, "y": 4}, {"patternId": "circle", "rotation": 270, "x": 3, "y": 5}, {"patternId": "arrow_up", "rotation": 180, "x": 3, "y": 6}, {"patternId": "circle", "rotation": 270, "x": 3, "y": 5}], "slot_sequence": ["RIGHT", "FRONT", "LEFT", "BACK", "BOTTOM", "BACK", "TOP", "RIGHT", "BOTTOM", "RIGHT"], "required_slots": ["RIGHT", "FRONT", "LEFT", "BACK", "BOTTOM", "TOP"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "arrow_left", "rotation": 90}, "BOTTOM": {"patternId": "arrow_up", "rotation": 90}, "FRONT": {"patternId": "J", "rotation": 270}, "BACK": {"patternId": "heart", "rotation": 180}, "LEFT": {"patternId": "triangle", "rotation": 90}, "RIGHT": {"patternId": "circle", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "arrow_left", "rotation": 90}, "BOTTOM": {"patternId": "arrow_up", "rotation": 90}, "FRONT": {"patternId": "J", "rotation": 270}, "BACK": {"patternId": "heart", "rotation": 180}, "LEFT": {"patternId": "triangle", "rotation": 90}, "RIGHT": {"patternId": "circle", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C498\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> S -> S -> W -> E -> E -> S -> S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=circle, rotation=180, flipVertical=true\n- step 2: patternId=J, rotation=0, flipVertical=true\n- step 3: patternId=triangle, rotation=90, flipVertical=true\n- step 4: patternId=heart, rotation=90, flipVertical=true\n- step 5: patternId=arrow_up, rotation=0, flipVertical=true\n- step 6: patternId=heart, rotation=90, flipVertical=true\n- step 7: patternId=arrow_left, rotation=0, flipVertical=true\n- step 8: patternId=circle, rotation=270, flipVertical=true\n- step 9: patternId=arrow_up, rotation=180, flipVertical=true\n- step 10: patternId=circle, rotation=270, flipVertical=true\n- allowed patternId values for this task: circle, J, triangle, heart, arrow_up, arrow_left, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C498"} +{"sample_id": "C499", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> S -> W -> S -> E -> N -> E -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "E", "S", "W", "S", "E", "N", "E", "E", "S"], "observed_path_faces": [{"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C499_path_sequence.png"}, "metadata": {"level_id": 499, "name": "Reconstruct 499", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-499.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["S", "smile", "2", "arrow_left", "4", "square"], "start_x": 1, "start_y": 1, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "S", "rotation": 90}, "BOTTOM": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "smile", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 270}, "LEFT": {"patternId": "4", "rotation": 90}, "RIGHT": {"patternId": "2", "rotation": 180}}, "bottom_faces": [{"patternId": "square", "rotation": 90, "x": 1, "y": 1}, {"patternId": "2", "rotation": 270, "x": 2, "y": 1}, {"patternId": "S", "rotation": 270, "x": 3, "y": 1}, {"patternId": "smile", "rotation": 180, "x": 3, "y": 2}, {"patternId": "2", "rotation": 0, "x": 2, "y": 2}, {"patternId": "square", "rotation": 180, "x": 2, "y": 3}, {"patternId": "smile", "rotation": 90, "x": 3, "y": 3}, {"patternId": "2", "rotation": 270, "x": 3, "y": 2}, {"patternId": "S", "rotation": 270, "x": 4, "y": 2}, {"patternId": "4", "rotation": 0, "x": 5, "y": 2}, {"patternId": "smile", "rotation": 270, "x": 5, "y": 3}], "slot_sequence": ["RIGHT", "TOP", "FRONT", "RIGHT", "BOTTOM", "FRONT", "RIGHT", "TOP", "LEFT", "FRONT"], "required_slots": ["RIGHT", "TOP", "FRONT", "BOTTOM", "LEFT"], "required_count": 5, "answer": {"faces": {"TOP": {"patternId": "S", "rotation": 90}, "BOTTOM": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "smile", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "4", "rotation": 180}, "RIGHT": {"patternId": "2", "rotation": 90}}}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 90}, "BOTTOM": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "smile", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "4", "rotation": 180}, "RIGHT": {"patternId": "2", "rotation": 90}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C499\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> S -> W -> S -> E -> N -> E -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=2, rotation=270, flipVertical=true\n- step 2: patternId=S, rotation=270, flipVertical=true\n- step 3: patternId=smile, rotation=180, flipVertical=true\n- step 4: patternId=2, rotation=0, flipVertical=true\n- step 5: patternId=square, rotation=180, flipVertical=true\n- step 6: patternId=smile, rotation=90, flipVertical=true\n- step 7: patternId=2, rotation=270, flipVertical=true\n- step 8: patternId=S, rotation=270, flipVertical=true\n- step 9: patternId=4, rotation=0, flipVertical=true\n- step 10: patternId=smile, rotation=270, flipVertical=true\n- allowed patternId values for this task: 2, S, smile, square, 4, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C499"} +{"sample_id": "C500", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> N -> S -> S -> W -> N -> W -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["E", "S", "N", "S", "S", "W", "N", "W", "S", "S"], "observed_path_faces": [{"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C500_path_sequence.png"}, "metadata": {"level_id": 500, "name": "Reconstruct 500", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-500.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["J", "smile", "1", "arrow_left", "arrow_up", "arrow_up"], "start_x": 2, "start_y": 1, "grid_width": 5, "grid_height": 6, "true_solution_faces": {"TOP": {"patternId": "J", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "smile", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 90}, "LEFT": {"patternId": "arrow_up", "rotation": 270}, "RIGHT": {"patternId": "1", "rotation": 90}}, "bottom_faces": [{"patternId": "arrow_up", "rotation": 270, "x": 2, "y": 1}, {"patternId": "1", "rotation": 180, "x": 3, "y": 1}, {"patternId": "smile", "rotation": 90, "x": 3, "y": 2}, {"patternId": "1", "rotation": 180, "x": 3, "y": 1}, {"patternId": "smile", "rotation": 90, "x": 3, "y": 2}, {"patternId": "arrow_up", "rotation": 0, "x": 3, "y": 3}, {"patternId": "arrow_up", "rotation": 90, "x": 2, "y": 3}, {"patternId": "smile", "rotation": 180, "x": 2, "y": 2}, {"patternId": "1", "rotation": 270, "x": 1, "y": 2}, {"patternId": "arrow_up", "rotation": 0, "x": 1, "y": 3}, {"patternId": "arrow_up", "rotation": 270, "x": 1, "y": 4}], "slot_sequence": ["RIGHT", "FRONT", "RIGHT", "FRONT", "LEFT", "BOTTOM", "FRONT", "RIGHT", "BOTTOM", "LEFT"], "required_slots": ["RIGHT", "FRONT", "LEFT", "BOTTOM"], "required_count": 4, "answer": {"faces": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "smile", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_up", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 0}}}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "smile", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_up", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 0}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C500\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> N -> S -> S -> W -> N -> W -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=1, rotation=180, flipVertical=true\n- step 2: patternId=smile, rotation=90, flipVertical=true\n- step 3: patternId=1, rotation=180, flipVertical=true\n- step 4: patternId=smile, rotation=90, flipVertical=true\n- step 5: patternId=arrow_up, rotation=0, flipVertical=true\n- step 6: patternId=arrow_up, rotation=90, flipVertical=true\n- step 7: patternId=smile, rotation=180, flipVertical=true\n- step 8: patternId=1, rotation=270, flipVertical=true\n- step 9: patternId=arrow_up, rotation=0, flipVertical=true\n- step 10: patternId=arrow_up, rotation=270, flipVertical=true\n- allowed patternId values for this task: 1, smile, arrow_up, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C500"} +{"sample_id": "C501", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> W -> S -> S -> W -> W -> N -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["W", "W", "W", "S", "S", "W", "W", "N", "E", "E"], "observed_path_faces": [{"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C501_path_sequence.png"}, "metadata": {"level_id": 501, "name": "Reconstruct 501", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-501.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": false}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": false}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["W", "arrow_left", "arrow_right", "J", "A", "square"], "start_x": 6, "start_y": 1, "grid_width": 8, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "W", "rotation": 0}, "BOTTOM": {"patternId": "square", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 0}, "BACK": {"patternId": "J", "rotation": 180}, "LEFT": {"patternId": "A", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}}, "bottom_faces": [{"patternId": "square", "rotation": 0, "x": 6, "y": 1}, {"patternId": "A", "rotation": 270, "x": 5, "y": 1}, {"patternId": "W", "rotation": 180, "x": 4, "y": 1}, {"patternId": "arrow_right", "rotation": 0, "x": 3, "y": 1}, {"patternId": "arrow_left", "rotation": 90, "x": 3, "y": 2}, {"patternId": "A", "rotation": 90, "x": 3, "y": 3}, {"patternId": "square", "rotation": 180, "x": 2, "y": 3}, {"patternId": "arrow_right", "rotation": 180, "x": 1, "y": 3}, {"patternId": "arrow_left", "rotation": 270, "x": 1, "y": 2}, {"patternId": "square", "rotation": 270, "x": 2, "y": 2}, {"patternId": "J", "rotation": 270, "x": 3, "y": 2}], "slot_sequence": ["LEFT", "TOP", "RIGHT", "FRONT", "LEFT", "BOTTOM", "RIGHT", "FRONT", "BOTTOM", "BACK"], "required_slots": ["LEFT", "TOP", "RIGHT", "FRONT", "BOTTOM", "BACK"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "W", "rotation": 0}, "BOTTOM": {"patternId": "square", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 0}, "BACK": {"patternId": "J", "rotation": 0}, "LEFT": {"patternId": "A", "rotation": 90}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}}}, "legacy_answer": {"TOP": {"patternId": "W", "rotation": 0}, "BOTTOM": {"patternId": "square", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 0}, "BACK": {"patternId": "J", "rotation": 0}, "LEFT": {"patternId": "A", "rotation": 90}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C501\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> W -> S -> S -> W -> W -> N -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=A, rotation=270, flipVertical=true\n- step 2: patternId=W, rotation=180, flipVertical=true\n- step 3: patternId=arrow_right, rotation=0, flipVertical=true\n- step 4: patternId=arrow_left, rotation=90, flipVertical=true\n- step 5: patternId=A, rotation=90, flipVertical=true\n- step 6: patternId=square, rotation=180, flipVertical=true\n- step 7: patternId=arrow_right, rotation=180, flipVertical=true\n- step 8: patternId=arrow_left, rotation=270, flipVertical=true\n- step 9: patternId=square, rotation=270, flipVertical=true\n- step 10: patternId=J, rotation=270, flipVertical=true\n- allowed patternId values for this task: A, W, arrow_right, arrow_left, square, J, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C501"} +{"sample_id": "C502", "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> N -> E -> E -> W -> S -> E -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.", "net_layout": "standard_cross", "roll_sequence": ["N", "E", "N", "E", "E", "W", "S", "E", "E", "S"], "observed_path_faces": [{"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "image_paths": {"blank_net_image": "images/blank_nets/open.png", "path_sequence_image": "images/path_sequences/C502_path_sequence.png"}, "metadata": {"level_id": 502, "name": "Reconstruct 502", "difficulty": 5, "move_count": 10, "tier": 5, "source_level_path": "levels/reconstruct/generated-502.json", "tier_label": "Difficulty 5"}, "description": "10-move reconstruct puzzle", "net_faces": [{"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": false}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": false}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": false}], "net_patterns": ["A", "G", "arrow_right", "F", "S", "C"], "start_x": 1, "start_y": 3, "grid_width": 7, "grid_height": 5, "true_solution_faces": {"TOP": {"patternId": "A", "rotation": 90}, "BOTTOM": {"patternId": "C", "rotation": 90}, "FRONT": {"patternId": "G", "rotation": 90}, "BACK": {"patternId": "F", "rotation": 90}, "LEFT": {"patternId": "S", "rotation": 180}, "RIGHT": {"patternId": "arrow_right", "rotation": 0}}, "bottom_faces": [{"patternId": "C", "rotation": 90, "x": 1, "y": 3}, {"patternId": "F", "rotation": 270, "x": 1, "y": 2}, {"patternId": "arrow_right", "rotation": 180, "x": 2, "y": 2}, {"patternId": "A", "rotation": 0, "x": 2, "y": 1}, {"patternId": "G", "rotation": 0, "x": 3, "y": 1}, {"patternId": "C", "rotation": 0, "x": 4, "y": 1}, {"patternId": "G", "rotation": 0, "x": 3, "y": 1}, {"patternId": "arrow_right", "rotation": 270, "x": 3, "y": 2}, {"patternId": "C", "rotation": 270, "x": 4, "y": 2}, {"patternId": "S", "rotation": 270, "x": 5, "y": 2}, {"patternId": "F", "rotation": 180, "x": 5, "y": 3}], "slot_sequence": ["BACK", "RIGHT", "TOP", "FRONT", "BOTTOM", "FRONT", "RIGHT", "BOTTOM", "LEFT", "BACK"], "required_slots": ["BACK", "RIGHT", "TOP", "FRONT", "BOTTOM", "LEFT"], "required_count": 6, "answer": {"faces": {"TOP": {"patternId": "A", "rotation": 90}, "BOTTOM": {"patternId": "C", "rotation": 90}, "FRONT": {"patternId": "G", "rotation": 90}, "BACK": {"patternId": "F", "rotation": 270}, "LEFT": {"patternId": "S", "rotation": 270}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}}}, "legacy_answer": {"TOP": {"patternId": "A", "rotation": 90}, "BOTTOM": {"patternId": "C", "rotation": 90}, "FRONT": {"patternId": "G", "rotation": 90}, "BACK": {"patternId": "F", "rotation": 270}, "LEFT": {"patternId": "S", "rotation": 270}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}}, "prompt": {"system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.", "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: top-down, with grid cell positions used to locate imprints; rotations are expressed in degrees clockwise.\n\n## 4. INPUT FIELDS\n- sample_id: C502\n- net_layout: standard_cross\n- difficulty: 5\n- move_count: 10\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> N -> E -> E -> W -> S -> E -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=F, rotation=270, flipVertical=true\n- step 2: patternId=arrow_right, rotation=180, flipVertical=true\n- step 3: patternId=A, rotation=0, flipVertical=true\n- step 4: patternId=G, rotation=0, flipVertical=true\n- step 5: patternId=C, rotation=0, flipVertical=true\n- step 6: patternId=G, rotation=0, flipVertical=true\n- step 7: patternId=arrow_right, rotation=270, flipVertical=true\n- step 8: patternId=C, rotation=270, flipVertical=true\n- step 9: patternId=S, rotation=270, flipVertical=true\n- step 10: patternId=F, rotation=180, flipVertical=true\n- allowed patternId values for this task: F, arrow_right, A, G, C, S, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":,\"rotation\":},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "__sample_id__": "C502"}