Add files using upload-large-folder tool

cube1/data/C485.json

@@ -0,0 +1,316 @@
+{
+  "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: <one-line JSON>\n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.",
+    "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: 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\":<string>,\"rotation\":<int>},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube1/data/C486.json

@@ -0,0 +1,316 @@
+{
+  "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: <one-line JSON>\n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.",
+    "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: 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\":<string>,\"rotation\":<int>},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube1/data/C487.json

@@ -0,0 +1,315 @@
+{
+  "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: <one-line JSON>\n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.",
+    "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: 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\":<string>,\"rotation\":<int>},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube1/data/C488.json

@@ -0,0 +1,315 @@
+{
+  "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: <one-line JSON>\n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.",
+    "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: 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\":<string>,\"rotation\":<int>},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube1/data/C489.json

@@ -0,0 +1,315 @@
+{
+  "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: <one-line JSON>\n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.",
+    "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: 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\":<string>,\"rotation\":<int>},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube1/data/C490.json

@@ -0,0 +1,316 @@
+{
+  "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: <one-line JSON>\n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.",
+    "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: 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\":<string>,\"rotation\":<int>},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube1/data/C491.json

@@ -0,0 +1,315 @@
+{
+  "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: <one-line JSON>\n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.",
+    "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: 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\":<string>,\"rotation\":<int>},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube1/data/C492.json

@@ -0,0 +1,315 @@
+{
+  "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: <one-line JSON>\n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.",
+    "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: 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\":<string>,\"rotation\":<int>},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube1/data/C493.json

@@ -0,0 +1,315 @@
+{
+  "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: <one-line JSON>\n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.",
+    "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: 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\":<string>,\"rotation\":<int>},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube1/data/C494.json

@@ -0,0 +1,314 @@
+{
+  "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: <one-line JSON>\n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.",
+    "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: 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\":<string>,\"rotation\":<int>},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube1/data/C495.json

@@ -0,0 +1,316 @@
+{
+  "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: <one-line JSON>\n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.",
+    "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: 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\":<string>,\"rotation\":<int>},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube1/data/C496.json

@@ -0,0 +1,316 @@
+{
+  "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: <one-line JSON>\n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.",
+    "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: 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\":<string>,\"rotation\":<int>},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube1/data/C497.json

@@ -0,0 +1,316 @@
+{
+  "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: <one-line JSON>\n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.",
+    "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: 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\":<string>,\"rotation\":<int>},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube1/data/C498.json

@@ -0,0 +1,316 @@
+{
+  "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: <one-line JSON>\n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.",
+    "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: 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\":<string>,\"rotation\":<int>},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube1/data/C499.json

@@ -0,0 +1,315 @@
+{
+  "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: <one-line JSON>\n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.",
+    "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: 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\":<string>,\"rotation\":<int>},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube1/data/C500.json

@@ -0,0 +1,314 @@
+{
+  "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: <one-line JSON>\n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.",
+    "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: 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\":<string>,\"rotation\":<int>},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube1/data/C501.json

@@ -0,0 +1,316 @@
+{
+  "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: <one-line JSON>\n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.",
+    "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: 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\":<string>,\"rotation\":<int>},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube1/data/C502.json

@@ -0,0 +1,316 @@
+{
+  "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: <one-line JSON>\n\nThe JSON object must follow the faces schema described in section 8 of the user prompt. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf a face cannot be uniquely determined from the inputs, output patternId=\"?\" and rotation=0 for that face. Always emit a complete FINAL_JSON line covering all six face keys; never refuse, never return prose only.",
+    "user": "## 1. TASK\nReconstruct the patternId and absolute rotation of every face of a cube from a roll-trace image.\nThe puzzle is solved when every output face matches the cube's true outer-surface configuration; faces that cannot be uniquely determined are reported with patternId=\"?\" and rotation=0.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. Faces are named by their orientation in the world frame: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- Cross net: the unfolded outer surface laid flat in a cross shape. Each cell of the cross is one face of the cube.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell.\n- Path imprint / bottom-face stamp: as the cube rolls, the face touching the ground stamps that face's pattern (rotated according to the roll) onto the grid cell it lay on. The path-sequence image shows these imprints from a top-down view.\n- patternId: the symbolic name of a face's printed pattern (e.g. \"smile\", \"triangle\", \"5\"). The literal string \"?\" denotes \"cannot be uniquely determined\".\n- rotation: an integer in {0, 90, 180, 270} measured clockwise from the pattern's upright orientation when the face is viewed from outside the cube.\n\n## 3. VISUAL LEGEND\n- Blank cross net image: shows the six face slots arranged in a cross with TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT labelled.\n- Path sequence image: a top-down grid showing the cube's start cell, the roll path, and the bottom-face imprints stamped along the path. Each imprint is the bottom-face pattern at the moment the cube rested on that cell, viewed from above (NOT viewed from underneath looking up).\n- Coordinate system: 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\":<string>,\"rotation\":<int>},\"BOTTOM\":{...},\"FRONT\":{...},\"BACK\":{...},\"LEFT\":{...},\"RIGHT\":{...}}}\n- faces: object with exactly six keys TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\n- patternId: string from the allowed list, or \"?\".\n- rotation: integer in {0, 90, 180, 270}; 0 when patternId is \"?\".\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube1/images/blank_nets/.gitkeep

@@ -0,0 +1 @@
+

cube1/images/path_sequences/.gitkeep

@@ -0,0 +1 @@
+

cube2/data/C425.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C425",
+  "name": "Goal Roll C425",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "I",
+          "rotation": 90
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "4",
+          "rotation": 90
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "?",
+          "rotation": 0
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "3",
+          "rotation": 180
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "I",
+          "rotation": 180
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "7",
+          "rotation": 90
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "I",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "4",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "3",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "I",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "7",
+        "rotation": 90
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 6,
+    "stepNumber": 7,
+    "patternId": "4",
+    "rotation": 0
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C425/initial_net.png",
+    "targetTopFaceImage": "../images/C425/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 7,
+    "targetRotationOffset": 270,
+    "levelId": 425,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-425.json"
+  },
+  "rollSequence": [
+    "S",
+    "W",
+    "W",
+    "E",
+    "E",
+    "N",
+    "N",
+    "N",
+    "W",
+    "S"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "S",
+      "W",
+      "W",
+      "E",
+      "E",
+      "N",
+      "N",
+      "N",
+      "W",
+      "S"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "I",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "4",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "3",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "I",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "7",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C425\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=4, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=3, rotation=180]\n[LEFT: patternId=I, rotation=180] [TOP: patternId=I, rotation=90] [RIGHT: patternId=?, rotation=0]\n  [FRONT: patternId=4, rotation=90]\n  [BOTTOM: patternId=7, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=3, rotation=180\n- LEFT: patternId=I, rotation=180\n- TOP: patternId=I, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=4, rotation=90\n- BOTTOM: patternId=7, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C426.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C426",
+  "name": "Goal Roll C426",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "triangle",
+          "rotation": 270
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "F",
+          "rotation": 270
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "X",
+          "rotation": 0
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "star",
+          "rotation": 270
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "9",
+          "rotation": 90
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "heart",
+          "rotation": 90
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "triangle",
+        "rotation": 270
+      },
+      "FRONT": {
+        "patternId": "F",
+        "rotation": 270
+      },
+      "RIGHT": {
+        "patternId": "X",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "star",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "9",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "heart",
+        "rotation": 90
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 2,
+    "stepNumber": 3,
+    "patternId": "star",
+    "rotation": 270
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C426/initial_net.png",
+    "targetTopFaceImage": "../images/C426/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 3,
+    "targetRotationOffset": 180,
+    "levelId": 426,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-426.json"
+  },
+  "rollSequence": [
+    "N",
+    "S",
+    "S",
+    "W",
+    "S",
+    "W",
+    "S",
+    "E",
+    "S",
+    "W"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "N",
+      "S",
+      "S",
+      "W",
+      "S",
+      "W",
+      "S",
+      "E",
+      "S",
+      "W"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "triangle",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "F",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "X",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "star",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "9",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "heart",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C426\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=star, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=star, rotation=270]\n[LEFT: patternId=9, rotation=90] [TOP: patternId=triangle, rotation=270] [RIGHT: patternId=X, rotation=0]\n  [FRONT: patternId=F, rotation=270]\n  [BOTTOM: patternId=heart, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=star, rotation=270\n- LEFT: patternId=9, rotation=90\n- TOP: patternId=triangle, rotation=270\n- RIGHT: patternId=X, rotation=0\n- FRONT: patternId=F, rotation=270\n- BOTTOM: patternId=heart, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C427.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C427",
+  "name": "Goal Roll C427",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "X",
+          "rotation": 90
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "star",
+          "rotation": 0
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "E",
+          "rotation": 90
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "X",
+          "rotation": 90
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "B",
+          "rotation": 270
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "D",
+          "rotation": 0
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "X",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "star",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "E",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "X",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "B",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "D",
+        "rotation": 0
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 5,
+    "stepNumber": 6,
+    "patternId": "X",
+    "rotation": 90
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C427/initial_net.png",
+    "targetTopFaceImage": "../images/C427/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 6,
+    "targetRotationOffset": 90,
+    "levelId": 427,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-427.json"
+  },
+  "rollSequence": [
+    "N",
+    "N",
+    "S",
+    "E",
+    "N",
+    "E",
+    "N",
+    "N",
+    "E",
+    "E"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "N",
+      "N",
+      "S",
+      "E",
+      "N",
+      "E",
+      "N",
+      "N",
+      "E",
+      "E"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "X",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "star",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "E",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "X",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "B",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "D",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C427\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=X, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=X, rotation=90]\n[LEFT: patternId=B, rotation=270] [TOP: patternId=X, rotation=90] [RIGHT: patternId=E, rotation=90]\n  [FRONT: patternId=star, rotation=0]\n  [BOTTOM: patternId=D, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=X, rotation=90\n- LEFT: patternId=B, rotation=270\n- TOP: patternId=X, rotation=90\n- RIGHT: patternId=E, rotation=90\n- FRONT: patternId=star, rotation=0\n- BOTTOM: patternId=D, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C428.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C428",
+  "name": "Goal Roll C428",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "star",
+          "rotation": 180
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "square",
+          "rotation": 270
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "A",
+          "rotation": 0
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "Q",
+          "rotation": 270
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "diamond",
+          "rotation": 0
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "R",
+          "rotation": 90
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "star",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "square",
+        "rotation": 270
+      },
+      "RIGHT": {
+        "patternId": "A",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "Q",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "diamond",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "R",
+        "rotation": 90
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 7,
+    "stepNumber": 8,
+    "patternId": "square",
+    "rotation": 270
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C428/initial_net.png",
+    "targetTopFaceImage": "../images/C428/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 8,
+    "targetRotationOffset": 90,
+    "levelId": 428,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-428.json"
+  },
+  "rollSequence": [
+    "S",
+    "N",
+    "N",
+    "E",
+    "N",
+    "E",
+    "N",
+    "N",
+    "W",
+    "W"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "S",
+      "N",
+      "N",
+      "E",
+      "N",
+      "E",
+      "N",
+      "N",
+      "W",
+      "W"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "star",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "square",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "A",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "Q",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "diamond",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "R",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C428\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=square, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=Q, rotation=270]\n[LEFT: patternId=diamond, rotation=0] [TOP: patternId=star, rotation=180] [RIGHT: patternId=A, rotation=0]\n  [FRONT: patternId=square, rotation=270]\n  [BOTTOM: patternId=R, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Q, rotation=270\n- LEFT: patternId=diamond, rotation=0\n- TOP: patternId=star, rotation=180\n- RIGHT: patternId=A, rotation=0\n- FRONT: patternId=square, rotation=270\n- BOTTOM: patternId=R, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C429.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C429",
+  "name": "Goal Roll C429",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "6",
+          "rotation": 270
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "P",
+          "rotation": 90
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "6",
+          "rotation": 180
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "E",
+          "rotation": 0
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "circle",
+          "rotation": 0
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "E",
+          "rotation": 0
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "6",
+        "rotation": 270
+      },
+      "FRONT": {
+        "patternId": "P",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "6",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "E",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "circle",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "E",
+        "rotation": 0
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 3,
+    "stepNumber": 4,
+    "patternId": "E",
+    "rotation": 270
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C429/initial_net.png",
+    "targetTopFaceImage": "../images/C429/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 4,
+    "targetRotationOffset": 270,
+    "levelId": 429,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-429.json"
+  },
+  "rollSequence": [
+    "W",
+    "N",
+    "N",
+    "W",
+    "N",
+    "N",
+    "S",
+    "N",
+    "S",
+    "E"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "W",
+      "N",
+      "N",
+      "W",
+      "N",
+      "N",
+      "S",
+      "N",
+      "S",
+      "E"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "6",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "P",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "6",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "E",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "circle",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "E",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C429\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=E, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=E, rotation=0]\n[LEFT: patternId=circle, rotation=0] [TOP: patternId=6, rotation=270] [RIGHT: patternId=6, rotation=180]\n  [FRONT: patternId=P, rotation=90]\n  [BOTTOM: patternId=E, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=E, rotation=0\n- LEFT: patternId=circle, rotation=0\n- TOP: patternId=6, rotation=270\n- RIGHT: patternId=6, rotation=180\n- FRONT: patternId=P, rotation=90\n- BOTTOM: patternId=E, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C430.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C430",
+  "name": "Goal Roll C430",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "heart",
+          "rotation": 90
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "?",
+          "rotation": 0
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "arrow_up",
+          "rotation": 0
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "9",
+          "rotation": 0
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "smile",
+          "rotation": 90
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "K",
+          "rotation": 90
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "heart",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "arrow_up",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "9",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "smile",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "K",
+        "rotation": 90
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 4,
+    "stepNumber": 5,
+    "patternId": "smile",
+    "rotation": 270
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C430/initial_net.png",
+    "targetTopFaceImage": "../images/C430/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 5,
+    "targetRotationOffset": 270,
+    "levelId": 430,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-430.json"
+  },
+  "rollSequence": [
+    "W",
+    "W",
+    "N",
+    "N",
+    "W",
+    "S",
+    "E",
+    "N",
+    "W",
+    "N"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "W",
+      "W",
+      "N",
+      "N",
+      "W",
+      "S",
+      "E",
+      "N",
+      "W",
+      "N"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "heart",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "arrow_up",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "9",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "smile",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "K",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C430\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=smile, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=9, rotation=0]\n[LEFT: patternId=smile, rotation=90] [TOP: patternId=heart, rotation=90] [RIGHT: patternId=arrow_up, rotation=0]\n  [FRONT: patternId=?, rotation=0]\n  [BOTTOM: patternId=K, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=9, rotation=0\n- LEFT: patternId=smile, rotation=90\n- TOP: patternId=heart, rotation=90\n- RIGHT: patternId=arrow_up, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=K, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C431.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C431",
+  "name": "Goal Roll C431",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "9",
+          "rotation": 180
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "arrow_left",
+          "rotation": 90
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "heart",
+          "rotation": 270
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "?",
+          "rotation": 0
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "1",
+          "rotation": 90
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "O",
+          "rotation": 0
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "9",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "arrow_left",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "heart",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "1",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "O",
+        "rotation": 0
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 8,
+    "stepNumber": 9,
+    "patternId": "1",
+    "rotation": 180
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C431/initial_net.png",
+    "targetTopFaceImage": "../images/C431/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 9,
+    "targetRotationOffset": 180,
+    "levelId": 431,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-431.json"
+  },
+  "rollSequence": [
+    "S",
+    "N",
+    "W",
+    "S",
+    "S",
+    "W",
+    "W",
+    "E",
+    "E",
+    "N"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "S",
+      "N",
+      "W",
+      "S",
+      "S",
+      "W",
+      "W",
+      "E",
+      "E",
+      "N"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "9",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "arrow_left",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "heart",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "1",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "O",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C431\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=1, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=?, rotation=0]\n[LEFT: patternId=1, rotation=90] [TOP: patternId=9, rotation=180] [RIGHT: patternId=heart, rotation=270]\n  [FRONT: patternId=arrow_left, rotation=90]\n  [BOTTOM: patternId=O, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=1, rotation=90\n- TOP: patternId=9, rotation=180\n- RIGHT: patternId=heart, rotation=270\n- FRONT: patternId=arrow_left, rotation=90\n- BOTTOM: patternId=O, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C432.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C432",
+  "name": "Goal Roll C432",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "9",
+          "rotation": 270
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "V",
+          "rotation": 180
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "?",
+          "rotation": 0
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "M",
+          "rotation": 90
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "4",
+          "rotation": 90
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "I",
+          "rotation": 0
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "9",
+        "rotation": 270
+      },
+      "FRONT": {
+        "patternId": "V",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "M",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "4",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "I",
+        "rotation": 0
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 5,
+    "stepNumber": 6,
+    "patternId": "I",
+    "rotation": 90
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C432/initial_net.png",
+    "targetTopFaceImage": "../images/C432/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 6,
+    "targetRotationOffset": 270,
+    "levelId": 432,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-432.json"
+  },
+  "rollSequence": [
+    "W",
+    "N",
+    "W",
+    "S",
+    "W",
+    "N",
+    "S",
+    "S",
+    "S",
+    "N"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "W",
+      "N",
+      "W",
+      "S",
+      "W",
+      "N",
+      "S",
+      "S",
+      "S",
+      "N"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "9",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "V",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "M",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "4",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "I",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C432\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=I, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=M, rotation=90]\n[LEFT: patternId=4, rotation=90] [TOP: patternId=9, rotation=270] [RIGHT: patternId=?, rotation=0]\n  [FRONT: patternId=V, rotation=180]\n  [BOTTOM: patternId=I, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=M, rotation=90\n- LEFT: patternId=4, rotation=90\n- TOP: patternId=9, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=V, rotation=180\n- BOTTOM: patternId=I, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C433.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C433",
+  "name": "Goal Roll C433",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "?",
+          "rotation": 0
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "diamond",
+          "rotation": 180
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "arrow_up",
+          "rotation": 180
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "S",
+          "rotation": 90
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "1",
+          "rotation": 90
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "diamond",
+          "rotation": 90
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "diamond",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "arrow_up",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "S",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "1",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "diamond",
+        "rotation": 90
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 3,
+    "stepNumber": 4,
+    "patternId": "1",
+    "rotation": 180
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C433/initial_net.png",
+    "targetTopFaceImage": "../images/C433/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 4,
+    "targetRotationOffset": 90,
+    "levelId": 433,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-433.json"
+  },
+  "rollSequence": [
+    "S",
+    "N",
+    "N",
+    "E",
+    "S",
+    "E",
+    "S",
+    "W",
+    "W",
+    "N"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "S",
+      "N",
+      "N",
+      "E",
+      "S",
+      "E",
+      "S",
+      "W",
+      "W",
+      "N"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "diamond",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "arrow_up",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "S",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "1",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "diamond",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C433\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=1, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=S, rotation=90]\n[LEFT: patternId=1, rotation=90] [TOP: patternId=?, rotation=0] [RIGHT: patternId=arrow_up, rotation=180]\n  [FRONT: patternId=diamond, rotation=180]\n  [BOTTOM: patternId=diamond, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=S, rotation=90\n- LEFT: patternId=1, rotation=90\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=arrow_up, rotation=180\n- FRONT: patternId=diamond, rotation=180\n- BOTTOM: patternId=diamond, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C434.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C434",
+  "name": "Goal Roll C434",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "?",
+          "rotation": 0
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "heart",
+          "rotation": 180
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "L",
+          "rotation": 90
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "8",
+          "rotation": 270
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "N",
+          "rotation": 270
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "G",
+          "rotation": 270
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "heart",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "L",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "8",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "N",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "G",
+        "rotation": 270
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 8,
+    "stepNumber": 9,
+    "patternId": "8",
+    "rotation": 180
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C434/initial_net.png",
+    "targetTopFaceImage": "../images/C434/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 9,
+    "targetRotationOffset": 90,
+    "levelId": 434,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-434.json"
+  },
+  "rollSequence": [
+    "E",
+    "N",
+    "W",
+    "N",
+    "W",
+    "S",
+    "S",
+    "W",
+    "W",
+    "N"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "E",
+      "N",
+      "W",
+      "N",
+      "W",
+      "S",
+      "S",
+      "W",
+      "W",
+      "N"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "heart",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "L",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "8",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "N",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "G",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C434\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=8, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=8, rotation=270]\n[LEFT: patternId=N, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=L, rotation=90]\n  [FRONT: patternId=heart, rotation=180]\n  [BOTTOM: patternId=G, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=8, rotation=270\n- LEFT: patternId=N, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=L, rotation=90\n- FRONT: patternId=heart, rotation=180\n- BOTTOM: patternId=G, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C435.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C435",
+  "name": "Goal Roll C435",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "7",
+          "rotation": 90
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "star",
+          "rotation": 270
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "arrow_right",
+          "rotation": 270
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "?",
+          "rotation": 0
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "U",
+          "rotation": 180
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "B",
+          "rotation": 180
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "7",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "star",
+        "rotation": 270
+      },
+      "RIGHT": {
+        "patternId": "arrow_right",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "U",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "B",
+        "rotation": 180
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 9,
+    "stepNumber": 10,
+    "patternId": "B",
+    "rotation": 90
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C435/initial_net.png",
+    "targetTopFaceImage": "../images/C435/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 10,
+    "targetRotationOffset": 270,
+    "levelId": 435,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-435.json"
+  },
+  "rollSequence": [
+    "S",
+    "W",
+    "S",
+    "E",
+    "E",
+    "S",
+    "W",
+    "E",
+    "W",
+    "S"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "S",
+      "W",
+      "S",
+      "E",
+      "E",
+      "S",
+      "W",
+      "E",
+      "W",
+      "S"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "7",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "star",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "arrow_right",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "U",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "B",
+      "rotation": 180
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C435\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=B, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=?, rotation=0]\n[LEFT: patternId=U, rotation=180] [TOP: patternId=7, rotation=90] [RIGHT: patternId=arrow_right, rotation=270]\n  [FRONT: patternId=star, rotation=270]\n  [BOTTOM: patternId=B, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=U, rotation=180\n- TOP: patternId=7, rotation=90\n- RIGHT: patternId=arrow_right, rotation=270\n- FRONT: patternId=star, rotation=270\n- BOTTOM: patternId=B, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C436.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C436",
+  "name": "Goal Roll C436",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "8",
+          "rotation": 0
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "4",
+          "rotation": 180
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "E",
+          "rotation": 180
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "5",
+          "rotation": 270
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "heart",
+          "rotation": 90
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "3",
+          "rotation": 0
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "8",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "4",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "E",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "5",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "heart",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "3",
+        "rotation": 0
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 0,
+    "stepNumber": 1,
+    "patternId": "heart",
+    "rotation": 0
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C436/initial_net.png",
+    "targetTopFaceImage": "../images/C436/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 1,
+    "targetRotationOffset": 180,
+    "levelId": 436,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-436.json"
+  },
+  "rollSequence": [
+    "E",
+    "S",
+    "W",
+    "E",
+    "S",
+    "S",
+    "W",
+    "N",
+    "N",
+    "S"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "E",
+      "S",
+      "W",
+      "E",
+      "S",
+      "S",
+      "W",
+      "N",
+      "N",
+      "S"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "8",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "4",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "E",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "5",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "heart",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "3",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C436\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=heart, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=5, rotation=270]\n[LEFT: patternId=heart, rotation=90] [TOP: patternId=8, rotation=0] [RIGHT: patternId=E, rotation=180]\n  [FRONT: patternId=4, rotation=180]\n  [BOTTOM: patternId=3, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=5, rotation=270\n- LEFT: patternId=heart, rotation=90\n- TOP: patternId=8, rotation=0\n- RIGHT: patternId=E, rotation=180\n- FRONT: patternId=4, rotation=180\n- BOTTOM: patternId=3, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C437.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C437",
+  "name": "Goal Roll C437",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "5",
+          "rotation": 90
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "2",
+          "rotation": 270
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "?",
+          "rotation": 0
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "N",
+          "rotation": 90
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "C",
+          "rotation": 180
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "U",
+          "rotation": 0
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "5",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "2",
+        "rotation": 270
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "N",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "C",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "U",
+        "rotation": 0
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 1,
+    "stepNumber": 2,
+    "patternId": "2",
+    "rotation": 270
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C437/initial_net.png",
+    "targetTopFaceImage": "../images/C437/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 2,
+    "targetRotationOffset": 90,
+    "levelId": 437,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-437.json"
+  },
+  "rollSequence": [
+    "W",
+    "N",
+    "W",
+    "S",
+    "S",
+    "W",
+    "W",
+    "E",
+    "N",
+    "N"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "W",
+      "N",
+      "W",
+      "S",
+      "S",
+      "W",
+      "W",
+      "E",
+      "N",
+      "N"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "5",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "2",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "N",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "C",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "U",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C437\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=2, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=N, rotation=90]\n[LEFT: patternId=C, rotation=180] [TOP: patternId=5, rotation=90] [RIGHT: patternId=?, rotation=0]\n  [FRONT: patternId=2, rotation=270]\n  [BOTTOM: patternId=U, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=N, rotation=90\n- LEFT: patternId=C, rotation=180\n- TOP: patternId=5, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=2, rotation=270\n- BOTTOM: patternId=U, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C438.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C438",
+  "name": "Goal Roll C438",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "T",
+          "rotation": 0
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "L",
+          "rotation": 0
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "smile",
+          "rotation": 90
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "circle",
+          "rotation": 180
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "N",
+          "rotation": 180
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "F",
+          "rotation": 270
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "T",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "L",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "smile",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "circle",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "N",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "F",
+        "rotation": 270
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 6,
+    "stepNumber": 7,
+    "patternId": "F",
+    "rotation": 90
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C438/initial_net.png",
+    "targetTopFaceImage": "../images/C438/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 7,
+    "targetRotationOffset": 270,
+    "levelId": 438,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-438.json"
+  },
+  "rollSequence": [
+    "E",
+    "S",
+    "W",
+    "E",
+    "E",
+    "S",
+    "N",
+    "S",
+    "E",
+    "N"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "E",
+      "S",
+      "W",
+      "E",
+      "E",
+      "S",
+      "N",
+      "S",
+      "E",
+      "N"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "T",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "L",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "smile",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "circle",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "N",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "F",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C438\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=F, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=circle, rotation=180]\n[LEFT: patternId=N, rotation=180] [TOP: patternId=T, rotation=0] [RIGHT: patternId=smile, rotation=90]\n  [FRONT: patternId=L, rotation=0]\n  [BOTTOM: patternId=F, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=circle, rotation=180\n- LEFT: patternId=N, rotation=180\n- TOP: patternId=T, rotation=0\n- RIGHT: patternId=smile, rotation=90\n- FRONT: patternId=L, rotation=0\n- BOTTOM: patternId=F, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C439.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C439",
+  "name": "Goal Roll C439",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "5",
+          "rotation": 90
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "?",
+          "rotation": 0
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "X",
+          "rotation": 180
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "D",
+          "rotation": 0
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "arrow_right",
+          "rotation": 90
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "Z",
+          "rotation": 270
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "5",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "X",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "D",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "arrow_right",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "Z",
+        "rotation": 270
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 7,
+    "stepNumber": 8,
+    "patternId": "Z",
+    "rotation": 180
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C439/initial_net.png",
+    "targetTopFaceImage": "../images/C439/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 8,
+    "targetRotationOffset": 270,
+    "levelId": 439,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-439.json"
+  },
+  "rollSequence": [
+    "N",
+    "N",
+    "W",
+    "S",
+    "N",
+    "W",
+    "W",
+    "W",
+    "S",
+    "E"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "N",
+      "N",
+      "W",
+      "S",
+      "N",
+      "W",
+      "W",
+      "W",
+      "S",
+      "E"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "5",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "X",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "D",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "arrow_right",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "Z",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C439\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=Z, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=D, rotation=0]\n[LEFT: patternId=arrow_right, rotation=90] [TOP: patternId=5, rotation=90] [RIGHT: patternId=X, rotation=180]\n  [FRONT: patternId=?, rotation=0]\n  [BOTTOM: patternId=Z, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=D, rotation=0\n- LEFT: patternId=arrow_right, rotation=90\n- TOP: patternId=5, rotation=90\n- RIGHT: patternId=X, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=Z, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C440.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C440",
+  "name": "Goal Roll C440",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "T",
+          "rotation": 90
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "arrow_up",
+          "rotation": 90
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "A",
+          "rotation": 270
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "W",
+          "rotation": 180
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "star",
+          "rotation": 0
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "?",
+          "rotation": 0
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "T",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "arrow_up",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "A",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "W",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "star",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 1,
+    "stepNumber": 2,
+    "patternId": "arrow_up",
+    "rotation": 0
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C440/initial_net.png",
+    "targetTopFaceImage": "../images/C440/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 2,
+    "targetRotationOffset": 180,
+    "levelId": 440,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-440.json"
+  },
+  "rollSequence": [
+    "E",
+    "N",
+    "E",
+    "N",
+    "E",
+    "E",
+    "S",
+    "W",
+    "N",
+    "N"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "E",
+      "N",
+      "E",
+      "N",
+      "E",
+      "E",
+      "S",
+      "W",
+      "N",
+      "N"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "T",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "arrow_up",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "A",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "W",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "star",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C440\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=arrow_up, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=W, rotation=180]\n[LEFT: patternId=star, rotation=0] [TOP: patternId=T, rotation=90] [RIGHT: patternId=A, rotation=270]\n  [FRONT: patternId=arrow_up, rotation=90]\n  [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=W, rotation=180\n- LEFT: patternId=star, rotation=0\n- TOP: patternId=T, rotation=90\n- RIGHT: patternId=A, rotation=270\n- FRONT: patternId=arrow_up, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C441.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C441",
+  "name": "Goal Roll C441",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "arrow_up",
+          "rotation": 0
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "B",
+          "rotation": 0
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "V",
+          "rotation": 0
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "?",
+          "rotation": 0
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "Z",
+          "rotation": 180
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "arrow_left",
+          "rotation": 270
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "arrow_up",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "B",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "V",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "Z",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "arrow_left",
+        "rotation": 270
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 7,
+    "stepNumber": 8,
+    "patternId": "Z",
+    "rotation": 270
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C441/initial_net.png",
+    "targetTopFaceImage": "../images/C441/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 8,
+    "targetRotationOffset": 90,
+    "levelId": 441,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-441.json"
+  },
+  "rollSequence": [
+    "E",
+    "E",
+    "S",
+    "S",
+    "N",
+    "E",
+    "W",
+    "W",
+    "S",
+    "S"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "E",
+      "E",
+      "S",
+      "S",
+      "N",
+      "E",
+      "W",
+      "W",
+      "S",
+      "S"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "arrow_up",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "B",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "V",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "Z",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "arrow_left",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C441\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=Z, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=?, rotation=0]\n[LEFT: patternId=Z, rotation=180] [TOP: patternId=arrow_up, rotation=0] [RIGHT: patternId=V, rotation=0]\n  [FRONT: patternId=B, rotation=0]\n  [BOTTOM: patternId=arrow_left, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=Z, rotation=180\n- TOP: patternId=arrow_up, rotation=0\n- RIGHT: patternId=V, rotation=0\n- FRONT: patternId=B, rotation=0\n- BOTTOM: patternId=arrow_left, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C442.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C442",
+  "name": "Goal Roll C442",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "5",
+          "rotation": 90
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "diamond",
+          "rotation": 90
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "5",
+          "rotation": 90
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "L",
+          "rotation": 90
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "5",
+          "rotation": 90
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "arrow_left",
+          "rotation": 0
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "5",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "diamond",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "5",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "L",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "5",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "arrow_left",
+        "rotation": 0
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 8,
+    "stepNumber": 9,
+    "patternId": "5",
+    "rotation": 270
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C442/initial_net.png",
+    "targetTopFaceImage": "../images/C442/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 9,
+    "targetRotationOffset": 270,
+    "levelId": 442,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-442.json"
+  },
+  "rollSequence": [
+    "W",
+    "N",
+    "W",
+    "N",
+    "E",
+    "N",
+    "E",
+    "N",
+    "W",
+    "N"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "W",
+      "N",
+      "W",
+      "N",
+      "E",
+      "N",
+      "E",
+      "N",
+      "W",
+      "N"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "5",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "diamond",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "5",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "L",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "5",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "arrow_left",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C442\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=5, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=L, rotation=90]\n[LEFT: patternId=5, rotation=90] [TOP: patternId=5, rotation=90] [RIGHT: patternId=5, rotation=90]\n  [FRONT: patternId=diamond, rotation=90]\n  [BOTTOM: patternId=arrow_left, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=L, rotation=90\n- LEFT: patternId=5, rotation=90\n- TOP: patternId=5, rotation=90\n- RIGHT: patternId=5, rotation=90\n- FRONT: patternId=diamond, rotation=90\n- BOTTOM: patternId=arrow_left, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C443.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C443",
+  "name": "Goal Roll C443",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "P",
+          "rotation": 270
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "K",
+          "rotation": 270
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "G",
+          "rotation": 0
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "?",
+          "rotation": 0
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "circle",
+          "rotation": 180
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "9",
+          "rotation": 270
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "P",
+        "rotation": 270
+      },
+      "FRONT": {
+        "patternId": "K",
+        "rotation": 270
+      },
+      "RIGHT": {
+        "patternId": "G",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "circle",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "9",
+        "rotation": 270
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 1,
+    "stepNumber": 2,
+    "patternId": "9",
+    "rotation": 270
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C443/initial_net.png",
+    "targetTopFaceImage": "../images/C443/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 2,
+    "targetRotationOffset": 180,
+    "levelId": 443,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-443.json"
+  },
+  "rollSequence": [
+    "E",
+    "E",
+    "S",
+    "S",
+    "N",
+    "E",
+    "N",
+    "W",
+    "N",
+    "E"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "E",
+      "E",
+      "S",
+      "S",
+      "N",
+      "E",
+      "N",
+      "W",
+      "N",
+      "E"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "P",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "K",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "G",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "circle",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "9",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C443\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=9, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=?, rotation=0]\n[LEFT: patternId=circle, rotation=180] [TOP: patternId=P, rotation=270] [RIGHT: patternId=G, rotation=0]\n  [FRONT: patternId=K, rotation=270]\n  [BOTTOM: patternId=9, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=circle, rotation=180\n- TOP: patternId=P, rotation=270\n- RIGHT: patternId=G, rotation=0\n- FRONT: patternId=K, rotation=270\n- BOTTOM: patternId=9, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C444.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C444",
+  "name": "Goal Roll C444",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "Z",
+          "rotation": 180
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "arrow_right",
+          "rotation": 180
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "D",
+          "rotation": 90
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "8",
+          "rotation": 0
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "1",
+          "rotation": 180
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "arrow_left",
+          "rotation": 90
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "Z",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "arrow_right",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "D",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "8",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "1",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "arrow_left",
+        "rotation": 90
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 9,
+    "stepNumber": 10,
+    "patternId": "arrow_right",
+    "rotation": 180
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C444/initial_net.png",
+    "targetTopFaceImage": "../images/C444/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 10,
+    "targetRotationOffset": 270,
+    "levelId": 444,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-444.json"
+  },
+  "rollSequence": [
+    "S",
+    "W",
+    "W",
+    "E",
+    "S",
+    "S",
+    "N",
+    "E",
+    "E",
+    "E"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "S",
+      "W",
+      "W",
+      "E",
+      "S",
+      "S",
+      "N",
+      "E",
+      "E",
+      "E"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "Z",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "arrow_right",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "D",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "8",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "1",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "arrow_left",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C444\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=arrow_right, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=8, rotation=0]\n[LEFT: patternId=1, rotation=180] [TOP: patternId=Z, rotation=180] [RIGHT: patternId=D, rotation=90]\n  [FRONT: patternId=arrow_right, rotation=180]\n  [BOTTOM: patternId=arrow_left, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=8, rotation=0\n- LEFT: patternId=1, rotation=180\n- TOP: patternId=Z, rotation=180\n- RIGHT: patternId=D, rotation=90\n- FRONT: patternId=arrow_right, rotation=180\n- BOTTOM: patternId=arrow_left, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C445.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C445",
+  "name": "Goal Roll C445",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "Q",
+          "rotation": 0
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "F",
+          "rotation": 90
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "R",
+          "rotation": 0
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "smile",
+          "rotation": 90
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "plus",
+          "rotation": 180
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "B",
+          "rotation": 0
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "Q",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "F",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "R",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "smile",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "plus",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "B",
+        "rotation": 0
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 1,
+    "stepNumber": 2,
+    "patternId": "B",
+    "rotation": 90
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C445/initial_net.png",
+    "targetTopFaceImage": "../images/C445/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 2,
+    "targetRotationOffset": 90,
+    "levelId": 445,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-445.json"
+  },
+  "rollSequence": [
+    "S",
+    "S",
+    "E",
+    "W",
+    "W",
+    "W",
+    "S",
+    "S",
+    "W",
+    "S"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "S",
+      "S",
+      "E",
+      "W",
+      "W",
+      "W",
+      "S",
+      "S",
+      "W",
+      "S"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "Q",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "F",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "R",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "smile",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "plus",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "B",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C445\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=B, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=smile, rotation=90]\n[LEFT: patternId=plus, rotation=180] [TOP: patternId=Q, rotation=0] [RIGHT: patternId=R, rotation=0]\n  [FRONT: patternId=F, rotation=90]\n  [BOTTOM: patternId=B, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=smile, rotation=90\n- LEFT: patternId=plus, rotation=180\n- TOP: patternId=Q, rotation=0\n- RIGHT: patternId=R, rotation=0\n- FRONT: patternId=F, rotation=90\n- BOTTOM: patternId=B, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C446.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C446",
+  "name": "Goal Roll C446",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "M",
+          "rotation": 270
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "triangle",
+          "rotation": 270
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "R",
+          "rotation": 90
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "3",
+          "rotation": 270
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "arrow_right",
+          "rotation": 270
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "diamond",
+          "rotation": 90
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "M",
+        "rotation": 270
+      },
+      "FRONT": {
+        "patternId": "triangle",
+        "rotation": 270
+      },
+      "RIGHT": {
+        "patternId": "R",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "3",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "arrow_right",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "diamond",
+        "rotation": 90
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 0,
+    "stepNumber": 1,
+    "patternId": "3",
+    "rotation": 270
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C446/initial_net.png",
+    "targetTopFaceImage": "../images/C446/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 1,
+    "targetRotationOffset": 180,
+    "levelId": 446,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-446.json"
+  },
+  "rollSequence": [
+    "S",
+    "W",
+    "S",
+    "S",
+    "W",
+    "S",
+    "S",
+    "E",
+    "N",
+    "W"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "S",
+      "W",
+      "S",
+      "S",
+      "W",
+      "S",
+      "S",
+      "E",
+      "N",
+      "W"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "M",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "triangle",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "R",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "3",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "arrow_right",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "diamond",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C446\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=3, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=3, rotation=270]\n[LEFT: patternId=arrow_right, rotation=270] [TOP: patternId=M, rotation=270] [RIGHT: patternId=R, rotation=90]\n  [FRONT: patternId=triangle, rotation=270]\n  [BOTTOM: patternId=diamond, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=3, rotation=270\n- LEFT: patternId=arrow_right, rotation=270\n- TOP: patternId=M, rotation=270\n- RIGHT: patternId=R, rotation=90\n- FRONT: patternId=triangle, rotation=270\n- BOTTOM: patternId=diamond, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C447.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C447",
+  "name": "Goal Roll C447",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "smile",
+          "rotation": 90
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "W",
+          "rotation": 90
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "L",
+          "rotation": 90
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "arrow_left",
+          "rotation": 180
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "Y",
+          "rotation": 180
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "arrow_up",
+          "rotation": 180
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "smile",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "W",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "L",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "arrow_left",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "Y",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "arrow_up",
+        "rotation": 180
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 4,
+    "stepNumber": 5,
+    "patternId": "W",
+    "rotation": 0
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C447/initial_net.png",
+    "targetTopFaceImage": "../images/C447/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 5,
+    "targetRotationOffset": 90,
+    "levelId": 447,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-447.json"
+  },
+  "rollSequence": [
+    "S",
+    "E",
+    "E",
+    "N",
+    "S",
+    "W",
+    "W",
+    "N",
+    "W",
+    "W"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "S",
+      "E",
+      "E",
+      "N",
+      "S",
+      "W",
+      "W",
+      "N",
+      "W",
+      "W"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "smile",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "W",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "L",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "arrow_left",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "Y",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "arrow_up",
+      "rotation": 180
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C447\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=W, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=arrow_left, rotation=180]\n[LEFT: patternId=Y, rotation=180] [TOP: patternId=smile, rotation=90] [RIGHT: patternId=L, rotation=90]\n  [FRONT: patternId=W, rotation=90]\n  [BOTTOM: patternId=arrow_up, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_left, rotation=180\n- LEFT: patternId=Y, rotation=180\n- TOP: patternId=smile, rotation=90\n- RIGHT: patternId=L, rotation=90\n- FRONT: patternId=W, rotation=90\n- BOTTOM: patternId=arrow_up, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C448.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C448",
+  "name": "Goal Roll C448",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "circle",
+          "rotation": 0
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "arrow_left",
+          "rotation": 0
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "X",
+          "rotation": 90
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "6",
+          "rotation": 0
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "4",
+          "rotation": 270
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "I",
+          "rotation": 270
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "circle",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "arrow_left",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "X",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "6",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "4",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "I",
+        "rotation": 270
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 1,
+    "stepNumber": 2,
+    "patternId": "6",
+    "rotation": 0
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C448/initial_net.png",
+    "targetTopFaceImage": "../images/C448/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 2,
+    "targetRotationOffset": 90,
+    "levelId": 448,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-448.json"
+  },
+  "rollSequence": [
+    "W",
+    "S",
+    "E",
+    "S",
+    "N",
+    "E",
+    "E",
+    "S",
+    "W",
+    "S"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "W",
+      "S",
+      "E",
+      "S",
+      "N",
+      "E",
+      "E",
+      "S",
+      "W",
+      "S"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "circle",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "arrow_left",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "X",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "6",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "4",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "I",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C448\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=6, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=6, rotation=0]\n[LEFT: patternId=4, rotation=270] [TOP: patternId=circle, rotation=0] [RIGHT: patternId=X, rotation=90]\n  [FRONT: patternId=arrow_left, rotation=0]\n  [BOTTOM: patternId=I, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=6, rotation=0\n- LEFT: patternId=4, rotation=270\n- TOP: patternId=circle, rotation=0\n- RIGHT: patternId=X, rotation=90\n- FRONT: patternId=arrow_left, rotation=0\n- BOTTOM: patternId=I, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C449.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C449",
+  "name": "Goal Roll C449",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "?",
+          "rotation": 0
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "square",
+          "rotation": 0
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "star",
+          "rotation": 270
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "smile",
+          "rotation": 270
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "smile",
+          "rotation": 270
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "N",
+          "rotation": 0
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "square",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "star",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "smile",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "smile",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "N",
+        "rotation": 0
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 1,
+    "stepNumber": 2,
+    "patternId": "smile",
+    "rotation": 180
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C449/initial_net.png",
+    "targetTopFaceImage": "../images/C449/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 2,
+    "targetRotationOffset": 180,
+    "levelId": 449,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-449.json"
+  },
+  "rollSequence": [
+    "E",
+    "S",
+    "W",
+    "W",
+    "E",
+    "E",
+    "S",
+    "W",
+    "N",
+    "E"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "E",
+      "S",
+      "W",
+      "W",
+      "E",
+      "E",
+      "S",
+      "W",
+      "N",
+      "E"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "square",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "star",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "smile",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "smile",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "N",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C449\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=smile, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=smile, rotation=270]\n[LEFT: patternId=smile, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=star, rotation=270]\n  [FRONT: patternId=square, rotation=0]\n  [BOTTOM: patternId=N, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=smile, rotation=270\n- LEFT: patternId=smile, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=star, rotation=270\n- FRONT: patternId=square, rotation=0\n- BOTTOM: patternId=N, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C450.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C450",
+  "name": "Goal Roll C450",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "C",
+          "rotation": 270
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "R",
+          "rotation": 90
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "Q",
+          "rotation": 270
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "8",
+          "rotation": 0
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "W",
+          "rotation": 0
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "?",
+          "rotation": 0
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "C",
+        "rotation": 270
+      },
+      "FRONT": {
+        "patternId": "R",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "Q",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "8",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "W",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 2,
+    "stepNumber": 3,
+    "patternId": "8",
+    "rotation": 270
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C450/initial_net.png",
+    "targetTopFaceImage": "../images/C450/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 3,
+    "targetRotationOffset": 90,
+    "levelId": 450,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-450.json"
+  },
+  "rollSequence": [
+    "S",
+    "W",
+    "E",
+    "S",
+    "S",
+    "W",
+    "N",
+    "W",
+    "N",
+    "E"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "S",
+      "W",
+      "E",
+      "S",
+      "S",
+      "W",
+      "N",
+      "W",
+      "N",
+      "E"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "C",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "R",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "Q",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "8",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "W",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C450\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=8, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=8, rotation=0]\n[LEFT: patternId=W, rotation=0] [TOP: patternId=C, rotation=270] [RIGHT: patternId=Q, rotation=270]\n  [FRONT: patternId=R, rotation=90]\n  [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=8, rotation=0\n- LEFT: patternId=W, rotation=0\n- TOP: patternId=C, rotation=270\n- RIGHT: patternId=Q, rotation=270\n- FRONT: patternId=R, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C451.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C451",
+  "name": "Goal Roll C451",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "I",
+          "rotation": 270
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "F",
+          "rotation": 270
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "U",
+          "rotation": 270
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "M",
+          "rotation": 90
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "circle",
+          "rotation": 270
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "arrow_down",
+          "rotation": 0
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "I",
+        "rotation": 270
+      },
+      "FRONT": {
+        "patternId": "F",
+        "rotation": 270
+      },
+      "RIGHT": {
+        "patternId": "U",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "M",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "circle",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "arrow_down",
+        "rotation": 0
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 4,
+    "stepNumber": 5,
+    "patternId": "circle",
+    "rotation": 90
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C451/initial_net.png",
+    "targetTopFaceImage": "../images/C451/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 5,
+    "targetRotationOffset": 90,
+    "levelId": 451,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-451.json"
+  },
+  "rollSequence": [
+    "W",
+    "W",
+    "N",
+    "S",
+    "W",
+    "E",
+    "N",
+    "N",
+    "E",
+    "N"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "W",
+      "W",
+      "N",
+      "S",
+      "W",
+      "E",
+      "N",
+      "N",
+      "E",
+      "N"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "I",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "F",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "U",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "M",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "circle",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "arrow_down",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C451\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=circle, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=M, rotation=90]\n[LEFT: patternId=circle, rotation=270] [TOP: patternId=I, rotation=270] [RIGHT: patternId=U, rotation=270]\n  [FRONT: patternId=F, rotation=270]\n  [BOTTOM: patternId=arrow_down, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=M, rotation=90\n- LEFT: patternId=circle, rotation=270\n- TOP: patternId=I, rotation=270\n- RIGHT: patternId=U, rotation=270\n- FRONT: patternId=F, rotation=270\n- BOTTOM: patternId=arrow_down, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C452.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C452",
+  "name": "Goal Roll C452",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "X",
+          "rotation": 0
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "W",
+          "rotation": 90
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "L",
+          "rotation": 180
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "4",
+          "rotation": 0
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "R",
+          "rotation": 180
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "B",
+          "rotation": 180
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "X",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "W",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "L",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "4",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "R",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "B",
+        "rotation": 180
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 9,
+    "stepNumber": 10,
+    "patternId": "X",
+    "rotation": 90
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C452/initial_net.png",
+    "targetTopFaceImage": "../images/C452/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 10,
+    "targetRotationOffset": 90,
+    "levelId": 452,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-452.json"
+  },
+  "rollSequence": [
+    "S",
+    "W",
+    "S",
+    "S",
+    "E",
+    "N",
+    "N",
+    "S",
+    "W",
+    "W"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "S",
+      "W",
+      "S",
+      "S",
+      "E",
+      "N",
+      "N",
+      "S",
+      "W",
+      "W"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "X",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "W",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "L",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "4",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "R",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "B",
+      "rotation": 180
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C452\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=X, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=4, rotation=0]\n[LEFT: patternId=R, rotation=180] [TOP: patternId=X, rotation=0] [RIGHT: patternId=L, rotation=180]\n  [FRONT: patternId=W, rotation=90]\n  [BOTTOM: patternId=B, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=4, rotation=0\n- LEFT: patternId=R, rotation=180\n- TOP: patternId=X, rotation=0\n- RIGHT: patternId=L, rotation=180\n- FRONT: patternId=W, rotation=90\n- BOTTOM: patternId=B, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C453.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C453",
+  "name": "Goal Roll C453",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "plus",
+          "rotation": 90
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "A",
+          "rotation": 270
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "O",
+          "rotation": 270
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "4",
+          "rotation": 180
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "?",
+          "rotation": 0
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "9",
+          "rotation": 270
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "plus",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "A",
+        "rotation": 270
+      },
+      "RIGHT": {
+        "patternId": "O",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "4",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "9",
+        "rotation": 270
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 6,
+    "stepNumber": 7,
+    "patternId": "4",
+    "rotation": 270
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C453/initial_net.png",
+    "targetTopFaceImage": "../images/C453/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 7,
+    "targetRotationOffset": 90,
+    "levelId": 453,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-453.json"
+  },
+  "rollSequence": [
+    "S",
+    "N",
+    "E",
+    "W",
+    "N",
+    "E",
+    "E",
+    "S",
+    "S",
+    "S"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "S",
+      "N",
+      "E",
+      "W",
+      "N",
+      "E",
+      "E",
+      "S",
+      "S",
+      "S"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "plus",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "A",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "O",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "4",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "9",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C453\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=4, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=4, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=plus, rotation=90] [RIGHT: patternId=O, rotation=270]\n  [FRONT: patternId=A, rotation=270]\n  [BOTTOM: patternId=9, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=4, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=plus, rotation=90\n- RIGHT: patternId=O, rotation=270\n- FRONT: patternId=A, rotation=270\n- BOTTOM: patternId=9, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}

cube2/data/C454.json

@@ -0,0 +1,246 @@
+{
+  "taskType": "roll_to_target_top_face",
+  "code": "C454",
+  "name": "Goal Roll C454",
+  "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.",
+  "instructions": {
+    "en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.",
+    "directionVocabulary": {
+      "N": "Up",
+      "S": "Down",
+      "W": "Left",
+      "E": "Right"
+    }
+  },
+  "initialCube": {
+    "net": {
+      "layout": "reconstruction_cross",
+      "faceOrder": [
+        "TOP",
+        "FRONT",
+        "RIGHT",
+        "BACK",
+        "LEFT",
+        "BOTTOM"
+      ],
+      "cells": [
+        {
+          "faceKey": "TOP",
+          "faceLabelZh": "TOP",
+          "row": 1,
+          "col": 1,
+          "patternId": "N",
+          "rotation": 270
+        },
+        {
+          "faceKey": "FRONT",
+          "faceLabelZh": "FRONT",
+          "row": 2,
+          "col": 1,
+          "patternId": "J",
+          "rotation": 0
+        },
+        {
+          "faceKey": "RIGHT",
+          "faceLabelZh": "RIGHT",
+          "row": 1,
+          "col": 2,
+          "patternId": "arrow_left",
+          "rotation": 90
+        },
+        {
+          "faceKey": "BACK",
+          "faceLabelZh": "BACK",
+          "row": 0,
+          "col": 1,
+          "patternId": "R",
+          "rotation": 270
+        },
+        {
+          "faceKey": "LEFT",
+          "faceLabelZh": "LEFT",
+          "row": 1,
+          "col": 0,
+          "patternId": "W",
+          "rotation": 90
+        },
+        {
+          "faceKey": "BOTTOM",
+          "faceLabelZh": "BOTTOM",
+          "row": 3,
+          "col": 1,
+          "patternId": "arrow_left",
+          "rotation": 0
+        }
+      ]
+    },
+    "solutionFaces": {
+      "TOP": {
+        "patternId": "N",
+        "rotation": 270
+      },
+      "FRONT": {
+        "patternId": "J",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "arrow_left",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "R",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "W",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "arrow_left",
+        "rotation": 0
+      }
+    }
+  },
+  "targetTopFace": {
+    "sourceObservationIndex": 7,
+    "stepNumber": 8,
+    "patternId": "N",
+    "rotation": 0
+  },
+  "answers": {
+    "directions": [],
+    "moveCount": 0,
+    "referenceValid": false
+  },
+  "imagePaths": {
+    "initialNetImage": "../images/C454/initial_net.png",
+    "targetTopFaceImage": "../images/C454/target_top_face.png"
+  },
+  "metadata": {
+    "difficulty": 5,
+    "tier": 5,
+    "targetStepNumber": 8,
+    "targetRotationOffset": 90,
+    "levelId": 454,
+    "moveCount": 10,
+    "sourceLevelPath": "levels/reconstruct/generated-454.json"
+  },
+  "rollSequence": [
+    "N",
+    "N",
+    "E",
+    "S",
+    "E",
+    "W",
+    "S",
+    "E",
+    "S",
+    "W"
+  ],
+  "observedPathFaces": [
+    {
+      "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
+    }
+  ],
+  "answer": {
+    "directions": [
+      "N",
+      "N",
+      "E",
+      "S",
+      "E",
+      "W",
+      "S",
+      "E",
+      "S",
+      "W"
+    ]
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "N",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "J",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "arrow_left",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "R",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "W",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "arrow_left",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <one-line JSON>\n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.",
+    "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C454\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=N, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n  [BACK: patternId=R, rotation=270]\n[LEFT: patternId=W, rotation=90] [TOP: patternId=N, rotation=270] [RIGHT: patternId=arrow_left, rotation=90]\n  [FRONT: patternId=J, rotation=0]\n  [BOTTOM: patternId=arrow_left, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=R, rotation=270\n- LEFT: patternId=W, rotation=90\n- TOP: patternId=N, rotation=270\n- RIGHT: patternId=arrow_left, rotation=90\n- FRONT: patternId=J, rotation=0\n- BOTTOM: patternId=arrow_left, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"<N|S|E|W>\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."
+  }
+}